The Edinburgh Gunners lock was dropped from the squad after a poor display in the defeat by France in their last RBS 6 Nations game.
But Murray was brought back into the squad along with Ross Beattie after Martin Leslie injured his neck and shoulder in training last Friday.
Gregor Townsend moves to stand-off in place of Brendan Laney who has an ankle injury.
And centre James McLaren returns to the international starting XV for the first time since the game against Wales last year.
Glasgow Warriors' back row forward Jason White also comes into the side as a direct replacement for flanker Leslie.
McGeechan had no qualms about keeping Murray in the starting line-up after the player performed well in training this week.
He said: "When Martin was injured, we thought the balance was right to look at the second row with Scott coming in.
"He offers us a great deal and we were looking at the best shape of the pack as we wanted it if Martin wasn't there.
"We thought then that it was obvious we should start with Scott.
"Scott has trained well with us this week. There is no doubt about that."
Scotland team to play Wales in Saturday's RBS 6 Nations Championship game at Murrayfield:
G Metcalfe (Glasgow); C Paterson (Edinburgh), J McLaren (Bordeaux-Begles), K Utterson (Borders), K Logan (Wasps); G Townsend (Borders), B Redpath (Sale, capt); T Smith (Northampton), G Bulloch (Glasgow), B Douglas (Borders), S Murray (Edinburgh), S Grimes (Newcastle), J White (Glasgow), S Taylor (Edinburgh), A Mower (Newcastle).
Replacements: R Russell (Saracens), G Kerr (Leeds), N Hines (Edinburgh), J Petrie (Glasgow), M Blair (Edinburgh), G Ross (Leeds), A Craig (Orrell).