The 24-year-old, who is the son of former England forward Andy Cole, joins Declan Gallagher (Livingston), Liam Polworth (Inverness CT), Jake Carroll (Cambridge United), Casper Sloth (Silkeborg), Jermaine Hylton (Solihull Moors) and Christopher Long (Blackpool) at Fir Park.
Cole was a youth player with Manchester City and can also count Bradford City and Fleetwood Town among his former clubs, on top of loan spells at Barnsley, MK Dons and Burton Albion.