The scrum-half currently plays with Edinburgh but will make the trip west over the summer.
Hart joined Edinburgh from Super Rugby side NSW Waratahs in 2013 and scored a try on his debut against Ulster, after coming off the bench at the Kingspan Stadium.
The New Zealand-born scrum-half has gone on to make 24 appearances for the GUINNESS PRO12 side, scoring five tries, including a crucial touchdown in his man of the match performance against the Ospreys at Myreside last month.
He played for the New Zealand under-20s in the 2008 IRB Junior World Championship, where he kept current All Blacks scrum-half Aaron Smith on the bench throughout the tournament.
Hart qualifies to play for Scotland through his Glasgow-born grandmother and was called up to the Scotland squad for last year's summer tour.
He made his debut for Vern Cotter's side as a substitute in the win over Canada in June and now has three caps for his country, after starting in the win over Argentina and coming off the bench in the defeat to South Africa.
Speaking to glasgowwarriors.org, Grayson said: "I'm really looking forward to working with Gregor (Townsend) and the other coaches at Scotstoun next season and competing for my place in the team.
"I've enjoyed the last couple of years in Edinburgh, but this is a new challenge for me, working with a different group of boys.
"I like the way Glasgow play and I feel their style of rugby will really suit my game.
"This is a great opportunity for me to continue to develop and improve as a rugby player in what looks like a great environment to be a part of.
"I'm excited about moving through to Glasgow in the summer, but at the moment I'm fully focused on trying to help Edinburgh finish in the top six."