Varney, who was born in Wales but qualifies for the Azzurri through his mother, made his debut for the Azzuri in a 2020 Autumn Nations Cup clash against Scotland. He has since made 32 appearances for the national side.
The move will see him link up with Ross Vintcent, another Italian international.
Varney left for France after first-team opportunities at Gloucester dried up following the signing of Wales scrum-half Tomos Williams midway through the 2023-24 season.
Rob Baxter, Chiefs director of rugby, said Varney is “still developing”.
“He’s a young player who at just 23 has already played a lot of rugby,” he said.
“He’s still developing as a player and moving towards what will be his prime years – both physically and mentally – as he keeps playing the level of rugby he is currently playing at.
“He’s got a very good set of basic, core skills around quality of kicking and passing as well as the tempo he can bring into the game.
“We’ve been very impressed with him in the meetings we’ve had, and he’s a guy who is very much on the upward curve in terms of his own performance.”
