The 32-year-old, who made his debut for the Scotland national team back in 2005, is due to move to his new club at the end of the month.
Head coach Richard Hill said: "John Andress, James Currie and Rob O'Donnell are all making big strides for us and we are naturally delighted to be able to sign a player of the quality of Euan Murray."
Murray added: "I looked at the ambition at Warriors and it's important to go somewhere where the set-up is right and everything is geared in the right direction, to bring success to the club.
"It's always been a difficult place to go as a player, so it will be nice to have the fans right behind me and it will definitely be a more enjoyable experience. I'm looking forward to getting out in front of the fans and showing what I can do."
The Glasgow-born player, who has 47 international caps to his name, has spent the last two months on loan to French side Agen.