The 34-year-old singer had been at loggerheads with the 'ME!' hitmaker since 2013 when Taylor accused Katy of having stolen some of her back-up dancers for her own tour, but earlier this year, the pair finally set aside their differences and even starred together in Taylor's music video for her latest single 'You Need to Calm Down'.
And now, Katy has explained they ended their feud at an industry event when the 'Chained to the Rhythm' star built up the courage to say sorry for her part in the six-year argument.
She said: "I sent her a literal olive branch and a note apologising for my part in all of it.
"[And then] I just went up to her and was like, 'Hey, it's been a long time and I think we've grown up a little bit, and I just wanted to say I'm sorry and I'm really here for you, and that I love you, and I hope that we can be friends in the future.' "
Katy said the pair then exchanged numbers and started texting, and soon managed to forge a new friendship where they can now "trust" each other.
Speaking to Australian radio show 'The Kyle & Jackie O Show', she said: "I can trust her and she can trust me, and we'll see each other in the halls of the music industry and not avoid each other. We'll embrace.
"It's amazing that we've had this opportunity to change, and I hope that other people can learn from it, too."
Meanwhile, 29-year-old Taylor recently revealed Katy had loved the idea for the 'You Need to Calm Down' music video - which sees them dressed as a burger and fries - because she wanted them to be a "symbol of redemption and forgiveness".
Taylor explained: "When I thought of this concept for the video and I wrote the treatment, I thought, 'I'm just gonna ask her if she'd be interested in this, but I would be totally fine if she'd rather keep it private.' But I sent her a long synopsis of the entire video and she was like, 'I would love for us to be a symbol of redemption and forgiveness!' "