Anscombe was limited to just five appearances for Bayonne in the Top 14 because of injury but believes he can make an impact in west Wales.
“I still have a huge desire to compete and to contribute on the field and help the team win matches,” he said.
“Competition brings the best out of players and that’s exactly what I want.
“My goal is to help push standards, share some of my experience and continue challenging myself.”
Anscombe started his career in his native New Zealand before moving to Cardiff in 2014.
He made his Wales debut – qualifying through his Welsh mother – a year later and won the last of his 42 caps against England in the 2025 Six Nations.
Anscombe moved to Ospreys in 2019 and spent four seasons with the club before moving to Gloucester and then Bayonne.
Scarlets finished 14th in the United Rugby Championship last season, above just Dragons and Zebre.
They have bolstered their squad for the coming campaign with Wales prop Corey Domachowski, once-capped New Zealand forward Cullen Grace, locks Harvey Cuckson, Alex Groves and Tom Allen, hookers John McKee and George Roberts and full-back Isaac Murray-Macgregor.
