The Wales U21 cap joined the Scarlets as an apprentice aged 18, before taking a two-year professional deal that expired this summer.
"Leaving is sad, but the style of rugby at Brive was irresistible," Davies said. "Before signing I spoke with my old teammate Barry Davies, who couldn't say enough good things about the club.
"To be able to play for Brive is the stuff of dreams which I am sure will make me a stronger player, both physically and mentally."
The Scarlets also lost first-choice scrum half Dwayne Peel in the summer, the Wales and Lions star having accepted an offer from Sale Sharks. But veteran Tongan scrum half Sililo Martens is joining the Scarlets, along with Ospreys youngster Martin Roberts.