The 31-year-old former Carlisle, QPR and Oldham midfielder was a member of the team relegated from the Scottish Premier League this season.
Crisis-hit Gretna could be wound up on Monday morning.
Murray remains hopeful the club who have been in administration since mid-March will survive, but admits the last couple of months have been taxing.
He told the Shrews' official website: "It was tough but it has stood me in good stead. Not getting paid and what was going on meant it was mentally tough.
"I worked hard all season despite those problems and I feel that I did well and think I've deserved this move.
"Quite a lot of players moved on but we were getting paid in the end and I think they should have a buyer very soon."