The 38-year-old has impressed greatly since taking over in July, with Raith five points off the top of the SPFL Championship.
Murray's backroom staff - which comprises assistant Paul Smith and player/first-team coach Laurie Ellis - have also agreed two-and-a-half year extensions with the Fife club.
Raith were also given further reason to celebrate yesterday after posting an £81,350 profit for the year ending June 2013 - figures which are due to a turnover of just over £1m.
"I'll wait for the local authority to lay on our open-top bus for the tour of Kirkcaldy," said Turnbull Hutton, the Raith chairman. "It is a massive achievement in the current climate to register a profit."