Bateman, 26, has spent two years at Exeter having joined the club in the summer of 2013 from London Welsh.
He made two starts for Exeter, one in the LV= Cup and one in the European Challenge Cup, as well as 15 replacement appearances.
Kitto, 23, moves to Welford Road having been part of Super Rugby's Chiefs' development squad this year.
"I was naturally frustrated with the lack of game time and I made no secret of that with Rob (Baxter, Exeter head coach), who understood," Bateman told the Exeter website.
"However, I can't speak highly enough of the Chiefs - it was a positive time for my career.
"Leicester will be a great challenge though. It is a great and historic club with a track record of bringing people in and doing good things."
Leicester director of rugby Richard Cockerill said: "Greg knows we have a very competitive group of front-rowers at this club, but he says he wants to come here and develop and test himself in that company.
"He has already gained useful Aviva Premiership experience and we look forward to his arrival this summer."
Cockerill also confirmed that scrum-half David Mele is to join French side Toulouse.
Leicester have signed Exeter hooker Greg Bateman and former New Zealand Under-20s scrum-half Jono Kitto.