On Friday night, the pop star and the NFL player, both 36, tied the knot at Madison Square Garden in a ceremony that was officiated over by Adam Sandler.
A billboard outside the venue read "JUST&T MARRIED" after the ceremony took place.
The couple were reported to have invited about 1000 guests, with celebrities including Gigi Hadid and Bradley Cooper, Graham Norton, Ed Sheeran, Hugh Grant and Ethan Hawke all in attendance.
Ahead of the event, the details were kept closely under wraps - with guests also reportedly told there was a strict "no phones" policy in place.
However, on Saturday some of the guests started spilling details about what unfolded inside the arena.
Speaking on Good Morning America, host George Stephanopoulos called the wedding "moving".
While discussing the wedding with co-hosts Robin Roberts and Michael Strahan just hours after the event wrapped up, Stephanopoulos said the ceremony was "so beautiful".
"It's hard to imagine that a place that big and a wedding with such stars could feel so personal and intimate … as intimate as it could possibly be given it was Madison Square Garden," he added.
Roberts agreed the event felt like "any wedding that you would attend," and also confirmed that the couple received a special performance from Stevie Nicks.
Roberts and Strahan also revealed the couple "wrote their own vows" and kept them in "little books" for the ceremony.
"It was their dream wedding, and it really was amazing," Strahan said.
"Congratulations to both of them."
Although she did not share any details of the nuptials, Swift's long-time close friend Selena Gomez posted a photo of herself posing in a gold gown on Instagram, which appeared to be the outfit she wore to the wedding.
Maren Morris shared a snap of one of the wedding keepsakes, posting a photo of an lace handkerchief that appeared to be gifted to guests at the celebration on Instagram.
The memento featured the couple's wedding logo - two overlapping T's framed by a pair of hearts - along with the date, July 3, 2026, and the location, New York City.
Underneath was a lyric from Swift's 2014 song Blank Space off her 1989 album, which read: "So it's gonna be forever…".
Sports commentator Rich Eisen and his wife, Suzy Shuster, also attended the event, with Eisen writing on Instagram: "Quite the NYC night. Storybook doesn't do the expression of love we witnessed justice."
Joann Jordan - the wife of personal trainer Rob Jordan - also shared a photo of them walking hand-in-hand up a red carpeted staircase and wrote: "An unforgettable evening in New York celebrating the beginning of a beautiful new chapter for our dear friends, Travis and Taylor. Love was in the air, the city was magical, and every detail was simply unforgettable!"
Since the wedding unfolded, more details have emerged about the details, including that Kelce's brother Jason's young daughters were flower girls, while Swift walked down the aisle as a string quartet played one of her own songs.
As the celebrations wrapped up, a string of stars were photographed leaving the venue in black cars including Reese Witherspoon, Brad Pitt, Steven Spielberg, Gracie Abrams, Millie Bobby Brown, Tom Brady, Tom Hanks, Sacha Baron Cohen and Phoebe Dynevor.
On Saturday, clean-up got under way at the arena, with crews seen beginning to dismantle the wedding set-up, unloading items including monogrammed set pieces and bars to chairs, booths, cushions and decorative trees.
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