The 32-year-old has been on loan this season with French Top 14 club Agen from Championship title favourites Newcastle.
He will move to Sixways next month, joining his third Premiership club after stints with Northampton and Newcastle, who were relegated from the top flight last season.
Glasgow-born Murray has won 47 caps and toured South Africa with the 2009 British and Irish Lions, although his trip was ended early by injury.
"I am really excited about getting involved with the Warriors," he said.
"I have done a fair bit of research and I realise that the club is definitely going in the right direction.
"It is an impressive team sheet, so I am looking forward to starting at Sixways."
Murray has been a key member of Scotland's pack since he made his Test debut against Romania in 2005.
He was part of the 2007 and 2011 World Cup campaigns, and he will join a Worcester squad who are coached, among others, by Murray's former Lions colleague Phil Vickery.
Worcester won their first game of the Premiership season last Friday, claiming a bonus-point victory over London Irish, while they drew with Gloucester and also ran Northampton, Leicester and Bath close in defeat.
- British and Irish Lions