The British & Irish Lion ace has enjoyed an impressive start to life at Sixways and has made seven appearances this season and quickly settled into his new surroundings.
Murray has endorsed the work going on and off the field at Warriors by opting to extend his stay and agreeing terms on a new long-term deal.
Glasgow-born Murray, 32, who also previously played at Northampton Saints, is one of the most fearsome and talented props in Northern Hemisphere rugby.
Murray's outstanding performances earned him a place on the British & Irish Lions tour to South Africa in 2009 and he featured for Scotland in both the 2007 and 2011 Rugby World Cups.
Head Coach Richard Hill said: "Euan has made a very good impression in the short space of time he has had here. It is not easy for someone coming in mid-season, but he has settled in remarkably well and is working well with the other front row forwards.
"He gives us that strength in depth in the front row which is something that clubs like Northampton and Leicester have always had. You have got to have a very powerful scrum to be successful in this league; you can't get away from that.
"Euan is good in very defence and carries strongly in the loose; he is a genuine all-round player. We are very pleased he has committed to the club because he is of true international class and up there with the very best of them in his position."