The 25-year-old, who made his debut for the All Blacks in the No 10 jersey against Australia in 2013, has signed a three-year contract with Bayonne and said he is not discounting returning to play in New Zealand again one day.
He has struggled for regular game time at first five-eighths with both Dan Carter and Colin Slade also at the Crusaders.
"I have absolutely loved my time here at Canterbury and the Crusaders, especially being a Christchurch boy," he said. "I've grown up with these teams and it's certainly been a tough decision to leave my hometown, but this is an exciting opportunity for the next part of my rugby career.
"At the moment all of my focus is on the season ahead. I am fully committed to the Crusaders for the rest of this season and will give my all for the team. I am also determined for a chance to be involved in this year's Rugby World Cup. If that doesn't happen then I will give my full commitment to the Canterbury team and enjoy playing another ITM Cup season."
Taylor last played for the All Blacks in 2013 against Japan. He has played 44 times for the Crusaders since making his debut in 2012.
Crusaders head Coach Todd Blackadder said Taylor's move would be a real loss to the Crusaders.
"Tom has an enormous amount of talent and a great rugby brain. His skills, versatility and attitude are greatly valued here and will be missed. We will be sad to see Tom go but respect and support his decision, and in the meantime we will enjoy having Tom around for the rest of this Super Rugby season and we will all be hoping to make it a special one for him."
Taylor will be set to face Crusaders teammate Dan Carter in France, as Carter is also heading for Europe next season having signed with Racing Metro.
