Bordeaux announced on their website this morning they had signed the 28-year-old for two seasons with his contract ending in June 2022.
Lam's acquisition comes as a replacement for former NRL star and Fijian powerhouse Semi Radradra who is leaving the Top 14 club after signing a deal with the Bristol Bears in the UK.
Lam turned heads in 2018 when he finished that year's Super Rugby season as the competition's top try-scorer, crossing the line 16 times.
He also knew his way to the line as a member of the All Blacks Sevens, scoring 54 tries and picking up a Commonwealth Games silver medal as a member of the 2014 squad at the Glasgow Games.
Despite his finishing abilities, Lam has never been able to crack the All Blacks with the likes of Rieko Ioane and more recently Sevu Reece and George Bridge picked ahead of him.
Lam's deal won't affect his current season with the Hurricanes.