The Kansas City Chiefs tight end, 35, and the pop superstar announced their engagement after two years of dating last month and the NFL star confessed that he was very "rattled" as he got down on one knee.
In a preview of his interview on Fox Sports, Kelce said: "She can tell the story. The palms were definitely sweating.
"I'm an emotional guy, so there were a few tears here and there. But it's been an exciting ride up to this day, and I can't wait to spend the rest of my life with her."
Kelce explained that the presence of Swift, 35, in his life has made him a "better person".
The sports star said: "She has brought excitement and a joy for life that made me a better man, made me a better person, and made me just that much more comfortable in who I am."
Kelce was described as a "human exclamation point" by the Shake it Off singer during her appearance on his New Heights podcast last month and he referred to that when discussing his legacy once his NFL career ends.
The tight end - who has started his 13th season with the Chiefs - said: "Um, that I was a good team-mate, I was a good person in the community. I just love what I do.
"I don't know. I'm not here for any other reasons. I just love coming in, playing football and giving people something to get excited for outside of their lives on Sundays. Hopefully they can see how much excitement I bring to my life, and they can bring that to others."
Meanwhile, Kelce explained that his life has been "fun" since he started dating Swift despite the increased scrutiny on him.
He said in a press conference: "I would say, ever since I've been dating Taylor life has been fun ... It's been exciting.
"Obviously a lot more eyes and I accept that, but I'm living life. Living on a high, I guess."
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