The 32-year-old joined Sale in 2011 and became the first Moldova international to play in the Premiership.
Cobilas is out of contract in the summer and has decided to move to France's Top 14.
"Vadim's got a great opportunity at his age, so it's a no-brainer for him," said Sale boss Steve Diamond.
President Laurent Marti announced the signing of the forward on their website and he joins Ireland fly-half Ian Madigan in moving to Bordeaux for next season.
Other players who are out of contract this summer have been free to speak to other clubs from 1 January, but Diamond has confirmed he is in advanced talks with David Seymour, Will Addison and Mark Jennings over new deals.
Scrum-half Chris Cusiter is understood to be considering his future, while hooker Tommy Taylor is reportedly a target for Wasps.
"There's no decision made on Tommy at the moment, he's not made his mind up," added Diamond.
Asked about recruitment for next season, he said: "We're actively out there now.
"I'm not in too much of a rush for it as we need to continue what we're doing here and if we lose three or four then we've got to replace them."
Prop Vadim Cobilas will leave Sale Sharks at the end of the season after he agreed a three-year deal with Bordeaux-Begles.