The San Francisco 49ers drafted Hyde in the second round of the 2014 draft two picks after the Bengals chose Jeremy Hill out of LSU.
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Hyde is a power back with speed who has run for 2,729 yards and 21 touchdowns in four NFL seasons.
Injuries were an issue for the 230-pounder early in his career, but Hyde played all 16 games last season and ran for 938 yards and eight touchdowns.
His signing should make fans who follow both the Buckeyes and the Browns happy, especially since Cleveland has shown an aversion to drafting Ohio State players over the past three decades.
Craig Powell, Darnell Sanders and Brian Robiskie are the only Buckeyes drafted by the Browns in the past 30 years.
There are no Ohio State grads on the Browns roster prior to Hyde’s signing.