The 23-year-old spent eight years at Boothferry Park before being released by Tigers boss Peter Taylor back in March.
He joined Colchester United towards the end of last season but failed to win a contract for next season's campaign despite impressing manager Phil Parkinson, and will now try his luck at Blundell Park.
Edwards has already spent time on trial at Boston United during the summer and even played 45 minutes, as United beat Goole 8-0 in a pre-season game last week.
Former Derby winger Matt O'Halloran is another trialist who will learn if he has done enough to win a contract at Blundell Park next week.
The 20-year-old, who never made a first-team appearance for Derby during his three seasons at the club, scored in Town's 1-0 victory over Lincoln last week.
He spent four months on loan at Burton Albion last season and has been looking to impress during this summer's pre-season.
Meanwhile, trialists Ouzo Osei and David Savage have both returned home and will not be offered contracts at Blundell Park.
