The versatile midfielder was released by Derby in January after just 14 appearances for the Pride Park outfit.
He was also banned from driving for 20 months after police found him asleep and unfit to drive in his car on the M1.
Malcolm, 27, had been linked with a move to MLS side FC Dallas, but will now hook up with former Rangers team-mates Ross McCormack, Stephen Hughes, Graeme Smith and Brian McLean at Fir Park.
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