President-elect Donald J. Trump, who has both derided Time magazine and pined for its approval, was named the publication’s person of the year on Thursday.

Mr. Trump also received the title in 2016, after his first presidential election victory, and now joins a group of 16 people who have been chosen more than once. The club includes the last three two-term presidents: Bill Clinton, George W. Bush and Barack Obama. (Franklin D. Roosevelt is the only person to have been given the title three times.)

Sam Jacobs, Time’s editor in chief, wrote in the magazine that the choice was not a difficult one: “On the cusp of his second presidency, all of us — from his most fanatical supporters to his most fervent critics — are living in the Age of Trump.”

Mr. Trump, who rang the opening bell at the New York Stock Exchange on Thursday morning, has had a tempestuous relationship with Time. After being named person of the year in 2016, he described the magazine as a “very important” publication and said it had granted him a “tremendous honor.”

But Mr. Trump, who had won a polarizing presidential race in which he lost the popular vote, bristled at Time’s cover, which described him as “president of the divided states of America.”

“I didn’t divide,” he objected in an interview with Matt Lauer on NBC’s “Today” show, adding: “We’re going to put it back together. And we’re going to have a country that’s very well healed.”

In 2017, Mr. Trump said he would most likely have been named person of the year for a second straight year if not for his unwillingness to sit for an interview and a photo shoot. Time pushed back on that claim.

But his frustration with the magazine has deeper roots. In 2011 he claimed that it had “lost all credibility” after it left him off a list of influential people. And as he grumbled in 2013 about another snub, he predicted that Time would soon cease to exist.

Still, Mr. Trump has plainly coveted the platform offered by the magazine and has said he grew up reading it. At one point, a fake 2009 cover story featuring Mr. Trump hung at his Mar-a-Lago estate in Palm Beach, Fla., The Washington Post reported in 2017.

Time has cast its annual choice as a reflection of a figure’s significance, not as a statement of approval.

Walter Isaacson, then the editor of Time, wrote in 1998 that the person of the year title recognized the individual “who most affected the news and our lives, for good or ill, and embodied what was important about the year, for better or for worse.”

The tradition — dismissed by some as a gimmicky self-promotion — dates to 1927, when Time selected Charles A. Lindbergh, who made the first nonstop solo trans-Atlantic airplane flight, as man of the year. (Time changed the name from man of the year to person of the year in 1999.)

The title has been bestowed on complex and even loathed figures in history, including Hitler and Stalin.

The title was shared by President Biden and his running mate, Kamala Harris, after their victory in the 2020 presidential race. Last year, Time selected the pop superstar Taylor Swift, who appeared on the magazine’s cover with one of her cats wrapped around her shoulders.

This year, Mr. Jacobs, the Time editor, wrote that Mr. Trump was “once again at the center of the world, and in as strong a position as he has ever been.”

And this year, the magazine’s cover — which showed Mr. Trump frowning slightly, his arm resting on his knee — did not describe him as “president of the divided states of America.”