The Tigers paid Gloucester an undisclosed fee to buy England international May out of the final year of his contract and the new arrival will be available for the start of the 2017/18 campaign.
At 27 years of age, the winger brings plenty of experience to Welford Road Stadium, having made more than 120 appearances for the Cherry and Whites, and O'Connor was pleased to have snapped up a quality player.
"We are absolutely delighted to add to the quality of our backs with the signing of Jonny May," he said. "He is a proven international, has played a lot of rugby at Premiership and Test level, and will add a lot of experience to the squad.
"He is an out-and-out finisher with an outstanding try-scoring record and I think he is a fantastic addition to the group."
As part of the deal, second-rower Ed Slater has moved in the opposite direction to join the Kingsholm club and O'Connor paid huge tribute to the 29-year-old's efforts.
He added: "Ed has been a fantastic servant to the club. He arrived as a young man and worked incredibly hard to put himself in the frame for England and to become club captain. We wish him all the best."