The 41-year-old joins the club from league One Airdrie where he has been manager since 2018.
Murray has also managed Dumbarton and St Mirrren and had a spell as assistant boss at Norwegian side Asker.
The former Hibs and Rangers player had led the Diamonds to the Championship play-off final this season after they finished second in the league – thanks in no small part to a 23-game unbeaten run – but they lost out to Queen’s Park.
A Raith spokesman said: “We hope that the Ian’s arrival at Stark’s Park is the turn of the first page in a new chapter in the club’s history after proving himself as the outstanding candidate in a an extremely strong pool of interviewees for the role.”
Steven MacDonald , chairman, added: “Ian is a creative hardworking ambitious manager, with an ability and foresight to make changes at the appropriate time, coupled with his determination to win.
“I feel we have made a great appointment and look forward to Ian bringing success to Raith Rovers”
Murray has signed a two year-contract at Stark’s Park.