Clarkson's contract with the Bantams was due to expire in the summer but he will leave the Coral Windows Stadium now after coming to an agreement with City.
Clarkson made one senior appearance for the club last season as a late substitute at Notts County on New Year's Day 2014.
The young forward scored four goals in pre-season this summer for the Bantams but, hindered by a hamstring problem, he failed to take part in any games for Phil Parkinson's men this campaign.
The former Hull City striker enjoyed loan periods at Ossett Town and Whitby Town earlier this season.
City chief Parkinson said: "There are currently one or two options out there for Lewis and we felt it was best for him to go and see if he could find first team football elsewhere.
"At this stage in his career, Lewis needs to be playing regularly. We wish him all the best for the future."