Accompanying the Instagram post is Swift's ballad So High School from the Tortured Poets Department album - rumoured to have been written about Kelce.
"I feel so high school every time I look at you," she sings.
The clip of the song finishes on the line "Are you gonna marry, kiss, or kill me?" which apparently is a reference to a 2016 interview in which Kelce chose to kiss Taylor in a game of Kiss, Marry, Kill.
"That was so magical and special to see," said Dr Iona Murphy, an adviser on last year's Victoria and Albert Museum's exhibition on Swift and a superfan who has written about Swift.
"A song that was written about Travis was now being used on the post. It's a nice full circle moment," said Dr Murphy, an English literature lecturer at Huddersfield University.
She said the caption to the Instagram announcement - "your English teacher and your gym teacher are getting married" – is also notable, as it refers to how the fans like to describe the couple.
"That's like a little joke in the fandom. You see it on social media. So it's like that was a little nod to the fans," she said.
In an interview with ABC's News 5 Cleveland station, Kelce's father, Ed, revealed that "Travis actually did the proposal... maybe two weeks, not quite two weeks ago".
He said this happened at a garden in the city of Lee's Summit, Missouri.
"He got her out there, they were about to go out to dinner, and he said, 'let's go out and have a glass of wine'... they got out there, and that's when he asked her, and it was beautiful," Ed Kelce said.
"They started FaceTiming me and their mother and her folks to make sure everybody knew. So, to see them together is great."