Terms were not disclosed, but the Cleveland Plain Dealer cited a source as saying the four-year deal is worth $8.25 million with 6.7 million guaranteed.
Manziel was selected with the 22nd overall pick of last month's draft and was the second of Cleveland's two first-round choices. Cornerback Justin Gilbert was the team's top pick at No. 8 overall.
The former Heisman Trophy winner had a brilliant two-year career at Texas A&M. He accounted for 9,989 yards of total offense with 93 touchdowns in 26 games for the Aggies and led the school to a record of 20-6.
Manziel was the first freshman to win the Heisman in 2012 and was a finalist as a sophomore. He threw for 3,706 yards as a freshman and 4,114 in his second year, totaling 63 touchdowns through the air and 22 interceptions in two years.