The highly-rated young defender is well thought of after spending last season impressing as part of last season's squad at Bostik League Premier outfit Worthing.
Last month, Cook had a trial with National League side Aldershot Town and after nothing came of it, Dowson persuaded him to come to The Beveree.
Cook originally signed for the Rebels after catching the eye while playing at Brighton University back in 2014 and made almost 100 appearances for the Sussex coast club.