The centre-back, who joined on a free transfer from Norwich 12 months ago, was under contract for another 18 months but has accepted a lump sum in order to terminate it early.
He will play alongside a former Iron teammate at Rugby Park, after Ben Gordon moved back to Ayrshire on loan on Wednesday.
Gordon spent the latter half of last season on loan at Glanford Park, after moving to North Lincolnshire alongside Nelson in the January transfer window.