Tuilagi joined the Basque outfit a year ago and had been linked with a move to Leicester and the rebel R360 league.
The 34-year-old made the last of his 60 England appearances in 2024 but is ineligible to represent his country as he plays his club rugby abroad.
"Ageing like a fine wine," Bayonne said on social media.
"Our English centre will continue to torment defences and attacks next season," they added.
Tuilagi is part of an illustruous rugby-playing family which includes brothers Henry and Alesana who featured for Samoa and nephew Posolo Tuilagi, who represents France.
Manu Tuilagi's Bayonne face Bordeaux-Begles in the Top 14 on Saturday and sit two points off leaders Pau after seven rounds of the season.