The 20-year-old, who trained with England ahead of this year's RBS 6 Nations, will make the move from Worcester Warriors after coming through the academy at Sixways.
"Worcester Warriors is all I've known to date, and I'll always be grateful to them for helping me achieve what I have in the game so far," Kvesic said in a Gloucester statement.
"The decision to leave has been a tough one to arrive at.
"However, when I spoke to Nigel Davies and he outlined Gloucester's plans for the future, and spoke about the squad he is assembling and where I would fit in, I was excited about the prospect and felt Gloucester would be the right place for me to help take my game to the next level.
"For the rest of the season though, I'm a Worcester player and will continue to give 100% every time I pull on the shirt to help us finish the season as strongly as possible."
Davies welcomed Kvesic's signing, saying: "Matt's a quality player, one we've admired for some time, and we're delighted that he's decided to commit to Gloucester Rugby.
"He's not yet 21, but already has considerable experience at Premiership level. The fact that England have called him up to train with them shows how much they think of him."
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