The 26-year-old has made 109 appearances (100 starts) for Glasgow Warriors since joining the club in 2010, scoring 29 tries so far and amassing 215 points.
The full-back marked his breakthrough season in 2011/12 by scoring a hat-trick away to reigning PRO12 champions Munster.
Hogg has since gone on to play a key role in many of the club's most memorable occasions, including the 2014/15 Guinness PRO12 title-winning campaign, and Glasgow's run to a first-ever European quarter-final in 2016/17.
The youngest Warrior to make 100 appearances, Hogg reached the milestone against Edinburgh at Scotstoun in May 2017.
He has earned 63 caps for his country and is a two-time British & Irish Lion and back-to-back Six Nations Player of the Championship (2016 and 2017).
Hogg said: "This is a decision that's taken a great deal of thought as I've loved my nine seasons at Glasgow Warriors. I said I would decide my next step for family and rugby reasons and feel now is the right time to gain new rugby experiences and push myself in different situations where I will be challenged and hopefully improve further.
"'M proud of what I have achieved with Glasgow Warriors and Scotland so far and would like to thank the club and Scottish Rugby for all their support. They have supported me when I had made my decision to move on and I know they did all they could and I'm grateful for their support.
"We are still less than halfway through my final season at the Warriors and, as current Conference A leaders in the Guinness PRO14 and second in our Heineken Champions Cup pool, there's a chance to do something special in my last season at the club. That's the send-off I want to give the club and the fans."
Glasgow Warriors Managing Director, Nathan Bombrys, said: “Stuart has been a great player and ambassador for our club and we're disappointed to lose an outstanding man.
"He has come through our Academy system, become a Centurion and won the PRO14 title with our club.
"He's used his time in Glasgow as a springboard to play 63 times for Scotland and earn the Six Nations Player of the Championship twice and represent the British and Irish Lions in 2013 and 2017.
"When the time comes he'll leave with our best wishes, but until then we know Stuart still has some unfinished business in Glasgow."
Glasgow Warriors Head Coach, Dave Rennie, added: "This is a great opportunity for Hoggy and he has our full support. He is a top man, loved by all and will be missed."