The news was first reported by Adam Caplan of SiriusXM radio.
Hoyer was released by Arizona on Monday afternoon, but Tom Brady's former understudy should challenge Jason Campbell for Cleveland's backup duties.
Hoyer, 27, signed with the Cardinals late last season after spending the previous three years in New England. In his lone start with Arizona -- a 27-13 loss to San Francisco -- Hoyer threw for 225 yards, one touchdown and an interception.
According to Caplan, Hoyer is expected to officially sign the deal on Friday. Two other teams were also interested in Hoyer's services.
The Browns were interested in dealing for the Michigan State product during the NFL Draft last month but were unable to reach a deal.
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