The Scotland fly-half has spent his entire senior career with the Warriors and was a Pro12 winner under Gregor Townsend in 2015.
Russell, who earned his 31st Scotland cap against New Zealand on Saturday, says his decision came from a desire to try something new, with the club announcing his departure in a lengthy statement.
Speaking to the Warriors' official website, he said: "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 Warriors (@GlasgowWarriors) November 19, 2017
Russell has been linked with a move to Top 14 side Racing 92, and Warriors managing director Nathan Bombrys admitted the number 10 has accepted a "lucrative" offer.
"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," he said.
"We respect his decision and when the time comes we will thank him for his contribution to the club. It has been great watching him develop and grow wearing a Glasgow Warriors shirt.
"We know he will be fully focused on trying to bring another trophy to Glasgow Warriors this season."
Photo by: Getty Images. Caption: Glasgow Warriors fly-half Finn Russell