The calls to the White House come at least once a week. “Murdoch here,” the blunt, accented voice on the other end of the line says.

For decades, Rupert Murdoch has used his media properties to establish a direct line to Australian and British leaders. But in the 44 years since he bought his first newspaper in the United States, he has largely failed to cultivate close ties to an American president. Until now.

Mr. Murdoch and President Trump — both forged in New York’s tabloid culture, one as the owner of The New York Post, the other as its perfect subject — have traveled in the same circles since the 1970s, but they did not become close until recently, when their interests began to align more than ever before.

Since Inauguration Day, Mr. Murdoch has talked regularly with Mr. Trump, often bypassing the White House chief of staff, Gen. John F. Kelly, who screens incoming calls. Mr. Murdoch has felt comfortable enough to offer counsel that others may shy away from, such as urging the president to stop tweeting and advising him to improve his relationship with Secretary of State Rex W. Tillerson. Mr. Murdoch also has weekly conversations with Mr. Trump’s son-in-law and senior adviser, Jared Kushner.

Before the news broke that Mr. Murdoch had agreed to sell vast parts of his 21st Century Fox to the Walt Disney Company for $52.4 billion, Mr. Trump called him to get his assurance that the Fox News Channel, the highly rated cable network and frequent bullhorn of the Trump agenda, would not be affected.

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On Dec. 14, the day the agreement was announced, Mr. Trump let the world know that he had made a congratulatory call to Mr. Murdoch. Sarah Huckabee Sanders, the White House press secretary, also passed along the president’s belief that the deal would be “a great thing” for jobs — a claim disputed by Wall Street analysts.

After decades of ups and downs, Mr. Trump now counts Mr. Murdoch as one of his closest confidants. The two titans made a show of their improved relationship in June 2016, when Mr. Murdoch visited Mr. Trump at the Trump International Golf Links Scotland before a group of reporters. They appeared together again at a black-tie dinner in May in honor of American and Australian veterans who fought side by side in World War II. Mr. Murdoch introduced the president as “my friend Donald J. Trump” before they engaged in a brief hug.

They are opposites in personal style, with Mr. Murdoch gruff and low-key, preferring schlubby newsrooms to Mr. Trump’s gilded towers and glitz. But they have much in common.

Both were born to wealth, but at a distance from the centers of power. Mr. Trump grew up in Jamaica, Queens, the son of a real estate developer content to earn his fortune in the boroughs outside Manhattan — so close but so far from glittering Midtown, where the son would make his name and his home. Mr. Murdoch, the son of a journalist who became the owner of a newspaper chain, spent his childhood in Melbourne, Australia. Mr. Murdoch, 86, and Mr. Trump, 71, are also alike in that they were both sent to military schools as boys before going on to outdo their fathers in the family businesses.

Although both men parlayed their inheritances into global power, they have stubbornly viewed themselves as outsiders at odds with the establishment. When Mr. Murdoch entered the British newspaper market in 1968, London society shunned him and his vulgar tabloids, The Sun and The News of the World, which he used to wound his enemies and advance his political interests. Mr. Trump withstood a similar wariness among the elite after he made himself a Manhattan player through his brazen deal making and hucksterism.

To make their way upward in New York, both men relied on a powerful friend, the lawyer Roy M. Cohn, a ruthless fixer who made his name in the 1950s as the chief counsel to Joseph McCarthy, the Red-baiting senator, before representing some of the city’s most powerful figures, including the mobster John Gotti and the New York Yankees owner George Steinbrenner.

Mr. Cohn connected Mr. Trump to Mr. Murdoch and the tabloid he bought in 1976, The New York Post. The upstart developer saw that he could benefit from the brash daily — especially its Page Six gossip column, which started a year after Mr. Murdoch became the paper’s owner.

“Trump was interested in specifically Rupert’s ownership of The Post, because Page Six is very important to his rising stature in New York City and branding efforts,” said Roger J. Stone Jr., a Republican operative who has known both men for decades.

Mr. Trump seemed to revel in the tabloid’s saucy coverage of his personal life. In 1989 and 1990, The Post turned out a series of front pages on Mr. Trump’s split from his first wife, Ivana Trump, and his affair with Marla Maples. The stream of headlines in bold block letters culminated in a quote attributed to Ms. Maples: “Best Sex I’ve Ever Had.”

Mr. Trump’s enthusiastic response to the planned Disney-Fox megadeal may have been lost in the swirl of Washington news had it not been for his vehement opposition to another recent attempt at media consolidation — AT&T‘s proposed $85.4 billion acquisition of Time Warner, the parent company of CNN, a frequent target of the president’s “fake news” complaints. While so far making no move on the Disney-Fox plan, the Justice Department has sued to block the AT&T-Time Warner deal on antitrust grounds in a rare instance of governmental interference in a merger of two companies that do not directly compete with each other.

Mr. Murdoch, whose ideology is more malleable than his critics realize, has long gained from his knack for placing himself close to power. In the 1980s, when he was cozy with Prime Minister Margaret Thatcher, his London tabloids took a pro-Tory stance. In 1997, his newspapers endorsed the Labor Party leader Tony Blair for prime minister.

Lance Price, a former Blair spokesman, referred to Mr. Murdoch as “effectively a member of Blair’s cabinet.” In turn, Mr. Murdoch faced little government scrutiny as he expanded his media empire to reach 40 percent of British newspaper readers and millions of television viewers through his stake in Sky, a pay TV service. But after a 2011 phone hacking scandal at the now-shuttered News of the World put a spotlight on his remarkable political influence, he found himself facing regulatory hurdles, and his $15 billion bid for a 61 percent stake of Sky came to nothing.

Even as Mr. Murdoch enjoyed an open invitation to 10 Downing Street, he found that his overtures to United States presidents mostly fell short. And before making their alliance, Mr. Murdoch and Mr. Trump had to put their old spats behind them.

Before the recent rapprochement, Mr. Murdoch privately called Mr. Trump “phony,” and accused him of exaggerating his net worth. For his part, Mr. Trump once threatened to sue Mr. Murdoch for libel after The Post reported that the storied Maidstone Club in East Hampton, N.Y., had denied him membership.

During much of the 2016 presidential campaign, Mr. Murdoch — who initially swooned over Jeb Bush — stood against Mr. Trump, declaring that he was “embarrassing his friends” and “the whole country.” The Wall Street Journal, Mr. Murdoch’s crown jewel, ran an editorial calling the candidate a “catastrophe.” The Post led with the headline “Don Voyage” and declared, “Trump is toast.”

Mr. Trump on Twitter: “Wow, I have always liked the @nypost but they have really lied when they covered me in Iowa.” He also the Journal: “Look how small the pages have become @WSJ,” he wrote. “Looks like a tabloid — saving money I assume!”

The Post ended up endorsing Mr. Trump, with reservations, in the New York primary, but refrained from endorsing either him or Hillary Clinton in the general election.

More recently, Mr. Murdoch expressed exasperation with Mr. Trump’s immigration policies. In response to the White House ban on travel of people from majority-Muslim nations, his company, 21st Century Fox, released a memo offering assistance to any employees hurt by the executive order and reminding them that “21CF is a global company, proudly headquartered in the U.S., founded by — and comprising at all levels of the business — immigrants.” In August, James Murdoch, the younger son of Mr. Murdoch and the chief executive of 21st Century Fox, condemned the president’s response to the riots in Charlottesville, Va.

The man partly responsible for the détente was another moneyed outsider who craved status and respect: Jared Kushner.

When Mr. Kushner bought The New York Observer in 2006, he wasted little time reaching out to Mr. Murdoch. “He wanted to be Murdoch,” said one person close to both men at the time. In early 2016, after a presidential debate during which Mr. Trump faced aggressive questioning from Megyn Kelly, then a Fox News anchor, the candidate sent Mr. Kushner to Mr. Murdoch on a media diplomacy mission.

Mr. Kushner’s wife, Ivanka Trump, is close friends with Mr. Murdoch’s third wife, Wendi Deng. Mr. Murdoch and Ms. Deng attended the Kushner-Trump wedding in 2009 at the Trump National Golf Club in Bedminster, N.J., and the Murdoch daughters, Grace and Chloe, served as flower girls.

Before Mr. Murdoch and Ms. Deng divorced in 2013, Mr. Kushner and Ms. Trump vacationed on Rosehearty, Mr. Murdoch’s 184-foot sailing yacht. In a further sign of the two families’ closeness, Ms. Trump took on the job of Murdoch trustee responsible for overseeing the two girls’ $300 million fortune — a role she gave up a month before President Trump took office.

In June 2016, when Mr. Trump appeared to be the inevitable Republican nominee, Mr. Murdoch made the visit to Trump International Golf Links Scotland. Completed in 2012 over the objections of nearby residents, the course lies 35 miles from the herring-fishing port of Rosehearty, the town left behind by the Murdoch clan when it emigrated to Australia in 1884.

Mr. Murdoch arrived with the former model Jerry Hall, his fourth wife, whom he married in March 2016. Under cloudy skies, the newlyweds toured the property in a golf cart large enough for four. Mr. Trump was at the wheel, with Ms. Hall seated beside him. Mr. Murdoch, wearing sunglasses, sat on a backward-facing rumble seat as they made their way to the Trump-refurbished Macleod House, a 15th century mansion, where they had dinner.

Mr. Trump’s mended relationship with Mr. Murdoch has not gone unnoticed by Time Warner executives, who wonder why AT&T’s attempt to buy the company has run into regulatory trouble at a time when the president has smiled on the Disney-Fox deal.

“If you look at the facts of our case, even before you heard the administration’s endorsement of the Disney-Fox deal, it was hard to understand how the Justice Department could reach a decision to block our deal,” Jeffrey L. Bewkes, the chief executive of Time Warner, said.

A spokesman for the White House, Raj Shah, said that Mr. Trump hadn’t spoken to Attorney General Jeff Sessions about the AT&T-Time Warner deal and that “no White House official was authorized to speak with the Department of Justice on this matter.”

The way CNN’s parent company views it, Fox News has adopted a role similar to the one played by Mr. Murdoch’s British tabloids when they helped advance the agendas of British leaders. As Mr. Blair learned, however, even a special relationship with the media baron can sour quickly. He and Mr. Murdoch — once so close that Mr. Blair was the godfather to Grace Murdoch — are no longer on speaking terms.

During the British government’s 2012 inquiry into the mogul’s political influence, the former prime minister described what it was like when a story subject falls out of favor with a Murdoch-controlled tabloid.

“Once they’re against you, that’s it,” Mr. Blair said. “It’s full on, full frontal, day in, day out, basically a lifetime commitment.”

Maggie Haberman contributed reporting.