World Cup-winning All Black joins Glasgow
The 35-year-old hooker will join the reigning Pro12 champions at the end of the current season for at least two years.
The former Crusaders forward, a World Cup winner in 2011 on home soil, had been in France since 2014.
"I've spent most of my career in New Zealand and had two years in France, so I'm thankful for the opportunity to join Glasgow Warriors next season and I'm looking forward to the new challenge," said Flynn.
"I jumped at the chance to join the Warriors after chatting to [coach] Gregor [Townsend] and I'm good friends with Sean Maitland and he couldn't say enough good things about Glasgow."
Flynn, who won 15 caps for the All Blacks, must first pass a medical and obtain a visa.
"Corey is a very experienced player, who has played at the highest level of the game," said Townsend.
"He will strengthen our leadership group, having captained Canterbury and the Crusaders, as well as the Junior All Blacks."
Townsend added: "Corey is also going to play an important role to help mentor some of our younger players and bring the best out of the other hookers in our squad.
"We're excited about his arrival next season, which will be the first time a Rugby World Cup winner has played for the Warriors."