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."

9 March 2017 Last updated at 17:03 GMT
The 19-year-old from Dublin is a competitive runner - but her chronic epilepsy means she has around 16 seizures a day, often during races.
When other competitors see her fall to the ground, they naturally believe she needs to go to hospital - even though she normally recovers immediately and in her case, there's no need for medical intervention.
Even though she's grateful for the public response, all Katie wants to do is carry on running.
When she told the neurologist who's treating her condition, he offered to become her running partner - and together they've become a marathon-running team.
Video by Andy Brownstone and Daniel Gordon

The homes are planned to be for social or mid-market rent and it is hoped they will all be completed by 2021.
Glasgow City Council's executive committee also approved £20m to improve existing housing.
Of this, £14m was announced last month as part of scheme to upgrade homes and make them available for social renting.
The £34m four-year improvement and repair scheme is also being funded with £20m from the Scottish government.
The funding to build homes is to be channelled through housing associations over the next four years.
Eight sites in the area have been identified for development.
As part of the strategy, Govanhill Housing Association has also committed £3.7m to new housing and repairs for the duration of the four year period.
Overall this means there are plans to invest more than £44m in housing in Govanhill over the next four years.
Councillor George Redmond: "This is an impressive document and points to the way ahead in Govanhill."
"Significant sums are being invested in Govanhill and it is great news that part of that money will go towards new housing.
"The council has been working exceptionally hard to turn things around in Govanhill and we are starting to see real progress being made."
He said that while the council was keen to work with all property owners in Govanhill, he warned the council would use power of compulsory purchase against those who refused to get on board with the plans.
Prop Vadim Cobilas will leave Sale Sharks at the end of the season after he agreed a three-year deal with Bordeaux-Begles.
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Katie Cooke has a lifestyle clash few others can rival.
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About 350 homes are to be built in the Govanhill area of Glasgow under a £6.4m council initiative to help "turn the area around".