The 24-year-old has endured a injury-plagued two-year stint at Scotstoun. But he showed enough in the 22 appearances he managed for the Warriors to attract the attention of the three-time champions of Europe.
It is understood Warriors granted Alainu’uese permission to move to the Top 14 outfit after agreeing a compensation package.
Warriors coach Dave Rennie – who has not been able to call on Alainu’uese at all this season – said: “It’s a decision that’s in the best interest of both the player and the club.
“Brian’s had a number of injuries over the last couple of years and we’ve not been able to play him as often as we would have liked, but he’s a good man, is very popular among the squad and will be missed.
“When he’s fit and firing he’s an excellent player and we wish him all the best in France.”
Alainu’uese said: “I’ve really enjoyed my two years in Glasgow. They’re a good bunch of boys and everyone made me feel very welcome. I hope the club goes on to have a lot of success in the future.”
Meanwhile, Glasgow have agreed to an early release for lead strength and conditioning coach Phil Healey to return home to New Zealand for personal reasons.
Healey will take up a position with Super Rugby side the Blues next month.