The 52-cap Wales scrum-half has signed a two-year deal with the Basque club, with the option of third, and will join his new team following the World Cup in September.
Phillips had fallen out of favour at the Ospreys after requesting to leave despite having three-years to run on a contract worth close to £1million.
Rhys Webb was selected ahead of the Test Lion following the RBS 6 Nations and the Ospreys also moved to sign Samoan international Kahn Fotuali'i.
"After continued requests from Mike over the last 18 months, we've agreed to let him go as soon as he can find another club," Ospreys director of rugby Scott Johnson said in April.
"It gets to a stage where within an organisation, anyone who doesn't want to be here will move on."
Welsh Rugby League side the Crusaders also revealed that they had attempted to persuade Phillips to switch codes and play in the Super League.
But he has instead followed in the footsteps of former Ospreys teammates and fellow Lions James Hook and Lee Byrne out of the Liberty Stadium and into the French top-flight.
The door was opened to Phillips after Bayonne's move for New Zealand scrum-half Byron Kelleher collapsed.
Phillips is just the latest star name to join the Basque club. Bayonne have already clinched the signatures of All Black trio Joe Rokocoko, Sione Lauki and Neemia Tialata, Australia's Mark Chisholm and French utility back Cédric Heymans.