The full-back has signed a two-and-a-half-year deal with the Top 14 club after opting to leave Agen, who were relegated from the top flight at the end of last season.
Elhorga was part of the Les Bleus squad for the 2006 November internationals, but did not receive a call-up for this year's RBS 6 Nations Championship or the World Cup.
The 30-year-old hopes his move to Bayonne will revive his international prospects.
"I am not the type of person to keep changing clubs, but I must now turn the page," he said.
"I have to bounce back to form and rediscover my international level with Bayonne."
Elhorga could be struggling to make France's squad for the 2008 Six Nations, which begins at the start of February.
He is still recovering from a knee operation he underwent last month.