Kelce had also talked about making her a beaded friendship bracelet, which were popular during the Eras Tour, and said he wanted to give her his phone number.
Swift said that podcast clip, which went viral, felt almost like "he was standing outside of my apartment, holding a boom box saying, 'I want to go on a date with you'".
Family and friends then started persuading her to take him up on his offer.
"My relatives, my cousins, were like, 'Please, please, please, he's amazing'. There were friends that were like, 'He's actually an amazing guy, he's so great'. There was a lot of people whispering in my ear about you."
She said it was exactly the moment she had "been writing songs about, wanting to happen to me since I was a teenager".
"It was wild, but it worked... He's the good kind of crazy," she said, calling her boyfriend "a human exclamation point".
Since the got together, the pair have been regularly spotted together, with Kelce often seen supporting Swift during her record breaking Eras tour.
He appeared at one of Swift's Eras Tour shows at Wembley Stadium on 23 June, where he arrived on stage wearing a top hat and tails as she prepared to perform the The Tortured Poets Department section of the show.
He then helped her prepare ahead of her song I Can Do It With A Broken Heart.