The 28-year-old, an integral part of the England team that claimed the World Cup in 2003, retired from rugby union in April because of a neck injury.
The former Northampton front-row forward will now move to Brive, the European champions in 1997, as he seeks to begin a career in coaching.
"My time had come at Saints and I needed a new challenge," Thompson, who spent his entire playing career at Franklin's Gardens, said.
"It's come in a different form now as a coach. Northampton's always my home but the great thing about rugby is that it's given me another opportunity."
Earlier this year, before being forced to retire, Thompson spoke to Brive regarding a possible move to the club, located in the Correze region of France.
He is looking forward to settling in France adding: "I'll keep a base in Northampton but we're moving out in September. I really want to buy into the culture out there.
"I'm looking forward to doing some recruitment and consultancy work on the business side of things with the company who own Brive rugby."