The 24-year-old flanker, who has won three England caps, has agreed a three-year deal at Sandy Park.
Former Worcester player Kvesic, whose contract ends this summer, has fallen out of favour at Kingsholm this season and has started just four league games for the Cherry and Whites.
He is the first new player that the Chiefs have signed this year.
"It's a great move for me," said Kvesic. "Over the last few years the Chiefs have shown they are one of the top teams in the country.
"I just felt it was the right time to have a new challenge in my career. Moving down to Exeter will maybe help re-ignite a few areas of my game."
After beginning his career at Worcester, Kvesic spent four years there before moving to Gloucester before the 2013-14 season.
Kvesic worked with Chiefs coach Rob Baxter in 2013 on England's tour of Argentina, where he won the first of his three caps.
He also worked with coach Ali Hepher in South Africa last summer and with Rob Hunter at Under-20s level, and has played with several of Exeter's England contingent, as part of both the Elite and Saxons squads.
"It's good that I know a number of people at the club already," he said. "Obviously I've talked to guys in the England set-up about the place and all of them have talked positively about the club.
"But I can't thank Gloucester enough for all that they have done for me. They're a great rugby club with fantastic supporters and I will always be grateful for the opportunities they've given me."
Gloucester's England forward Matt Kvesic will join Premiership rivals Exeter Chiefs in the summer.