The 30-year-old England international will join the Devon club from the start of next season after agreeing a three-year contract with the Chiefs.
Waldrom joined Tigers in the summer of 2010 and has made just over 100 appearances for the club as well as winning five England caps.
"It's a fresh challenge for me,” said New Zealand-born Waldrom.
"I've had four fantastic years at Leicester and experienced so many high points. A lot of what I have achieved in the game has come from my time playing there, so I owe them and the supporters an awful lot.
"I've made a lot of good mates who I will no doubt stay in touch with, but when I spoke to Rob Baxter I liked what he had to say about the [Exeter] club.”
Tigers director of rugby Richard Cockerill said: “Thomas has been very good for us for four seasons and will continue to be for the remainder of this season. When he does go in the summer he will leave with our best wishes.”