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Manager Nigel Spackman had been keen to bolster his defence after The Lions humiliating 5-1 defeat away to Chesterfield last weekend and moved for the Scottish international after a recommendation from Ray Wilkins.
Malcolm, who is currently the Glasgow club's longest-serving player, had been attracting interest from Derby County and Swansea City but a strong factor in his decision to come to The Den is the presence of three former Rangers players - Tom Brighton, Maurice Ross and Derek McInnes.
Malcolm is in his final year of his contract at Ibrox but has not featured in new manager Paul Le Guen's first-team plans, having been omitted from the club's pre-season tour of South Africa.