The striker has signed a two-year contract with the option of a third season after leaving Aberdeen.
A move fell apart at the last minute in July, but May's representatives, the club and Aberdeen finally came to an agreement four days before the end of the transfer window.
The 26-year-old hit 27 goals in his final season for Saints, which culminated in them winning the 2014 Scottish Cup, the club's only piece of major silverware.
The Perth-born forward told St Johnstone's Twitter account: "It's brilliant to eventually get it over the line. It's been a long time coming. It's nice to just walk into the stadium and see familiar faces. It's somewhere I pretty much grew up. It's great to be back."
Tommy Wright had declared his hope that a deal could be resurrected earlier in the summer and May admitted the manager's faith was a big factor in his return following spells at Sheffield Wednesday, Preston and Pittodrie.
"Obviously that was a big pull as well as the club in general and the fans as well," he said.
"Tommy has made it obvious that I was the man he wanted to get in and that's more than you could ask for as a player.
"That was a big thing for me as well, coming back to play for someone I know well, and a club and formation and players that I know.
"It all made it the right thing for me and the club as well.
"Hopefully we can have more success like we have had in the past, and for the fans as well.
"I still get stopped in the street by fans when I'm in Perth, so it's nice to know how high you are held by them. The success is not just for the players and manager, it's for the fans as well."