On Thursday, the publication tweeted an image of the cover which sees Mr Buttigieg and his husband, Chasten Buttigieg, standing outside a quintessentially white picket-fenced home, wearing co-coordinating blue shirts and trousers.
The magazine’s cover line reads: “The unlikely, untested and unprecedented campaign of Mayor Pete Buttigieg.”
The pair, who married in June 2018, are the first same-sex couple to pose together on the cover of the magazine since an edition of the publication was dedicated to equal marriage in 2013.
While Mr Buttigieg's run for the presidency divides the public, several Twitter users have praised the publication’s cover.
“If you only knew what this means to so many... And what it would have meant to 12 year old me,” wrote one user.
Another added: “Inspiring! Pete Buttigieg’s candidacy IS progress [sic]!”
“This is amazing,” added another.
The Time magazine article explores Mr Buttigieg’s rise to fame and his relationship with Chasten, recounting how they met on an online dating app while the politician was serving as mayor, and his subsequent decision to come out while in office.
Speaking to Time, Mr Buttigieg says that he often heard homophobic comments from fellow officers while serving in the armed forces, long before he opened up about his sexuality in 2015.
However, he adds that many of his former colleagues have expressed their support since announcing his run for Office.
“I bet some of them still go back and tell gay jokes because that’s their habit, you know? Bad habits and bad instincts is not the same as people being bad people," he says.
Mr Buttigieg continues, explaining that he is a great believer in the “power of redemption and forgiveness” after seeing “once-disapproving parents dance at their gay son’s wedding and homophobic military officers take back their words”.
“We’ve got to get away from this kill-switch mentality that we see on Twitter,” he notes.
“This idea that we just sort people into baskets of good and evil ignores the central fact of human existence, which is that each of us is a basket of good and evil.
“The job of politics is to summon the good and beat back the evil.”
Late in the interview, his husband opens up about becoming homeless after coming out to his parents.
“Being gay was not culturally acceptable where I grew up, mostly for a lack of understanding, and so my family and I were just at a crossroads, and we didn’t really know how to talk to one another,” the 29-year-old comments.
The 37-year-old mayor of South Bend, Indiana officially launched his 2020 presidential campaign in April in the hope to become the youngest-ever and first openly gay commander in chief.
Announcing his run for office in Indiana, he told the crowd in attendance: "My name is Pete Buttigieg. They call me Mayor Pete. I am a proud son of South Bend, Indiana. And I am running for president of the United States.
"I recognise the audacity of doing this as a Midwestern millennial mayor. More than a little bold — at age 37— to seek the highest office in the land."
In April, Mr Buttigieg shared his decision to not speak openly about his sexuality until the age of 33.
“It took me plenty of time to come out to myself,” Mr Buttigieg told TV host Rachel Maddow on her MSNBC show.
“I did not, the way you did or my husband did, figure out at such an early age. I probably should have. There were certainly plenty of indications by the time I was 15 or so that I could point back [and say] ‘yeah, this kid’s gay.’
“I guess I just really needed to not be. There’s this war that breaks out inside a lot of people when they realise that they might be something they’re afraid of. It took me a very long time to resolve that.”
On Thursday, The Washington Post published a profile piece of Mr Buttigieg in which he opened up about the criticism the couple received after kissing at his husband’s campaign launch in April.
“[It was] the level of intimacy we were comfortable with in that moment,” Mr Buttigieg explained.
“I’m not surrounded by people telling me not to be myself, and if I were, I’d ask them to find a different project to work on.”
Mr Buttigieg is running for the Democratic presidential nomination in the upcoming primary. Other frontrunners include Elizabeth Warren, Cory Booker, Kamala Harris and Joe Biden.
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