It was Perry who ended the row when she sent Swift a package containing an olive branch and a handwritten note shortly before she started her new tour in Arizona.
The Look What You Made Me Do singer posted a video to her Instagram story showing the note, which read: “Hey old friend.”
The video was captioned “Thank you Katy”.
Swift said in the video: “I just got to my dressing room and found this actual olive branch.
“This means so much to me.”
Swift and Perry reportedly fell out in a row over backing dancers and both have addressed the feud through their music.
Swift’s Bad Blood is thought to be about Perry, while Perry’s Swish Swish is said to be about Swift.
Swift is also thought to have written songs about her ex partners, including British stars Harry Styles and Tom Hiddleston.
Her tour will support her worldwide hit album Reputation.
The first night at the University of Phoenix Stadium saw British singer Charli XCX opening for Swift, performing her hit tracks Boom Clap and Boys to the rapturous crowd.
Another famous member of Swift’s “squad”, Camila Cabello, also took part.
Swift will perform in Manchester, London and Dublin in June.