The 25-year-old, who played in Saturday’s dramatic 22-17 loss to New Zealand at BT Murrayfield, has been linked with a big-money move to France and it is believed that Paris club Racing 92 are favourites to land his signature.
Russell is one of Scotland’s star players and it will be a blow to the SRU that he will be outwith its player management structure heading towards the 2019 World Cup in Japan.
However, with his contract up at the end of the season it has been widely rumoured that he would be moving on to test himself outside Scotland.
Russell, who spent time on this year’s Lions tour as injury cover, said: “I’ve really enjoyed my five years at Glasgow Warriors. I would like to thank every player, coach and member of the backroom staff for making it so special.
“During my time at the club I’ve really developed as a player and I’ve been called up to the Scotland and British and Irish Lions squads.
“I’ve shared so many fantastic moments with people who are now friends for life and to do it in front of the amazing Glasgow Warriors supporters at Scotstoun has been a dream come true. I’ve always wanted to experience as much as I can during what is a short rugby career.
“It was obviously a difficult decision to leave Glasgow, but I have the opportunity to take myself out of my comfort zone and experience a new culture and type of rugby.
“However, I am fully focused on Glasgow Warriors and will do everything I can to make my final season at Scotstoun a successful one.”
Glasgow managing director Nathan Bombrys added: “Our club has an excellent track record of retaining our key players in recent years. However, in this instance Finn has decided to move on and accept a lucrative opportunity at another club.”