Shaw has spent the season on the practice squad, but will sign a contract on Friday and join the active roster on Saturday, according to a report from Mary Kay Cabot of The Plain-Dealer in Cleveland.
The Browns signed Shaw to their practice squad in August after he went undrafted out of South Carolina. He is the winningest quarterback in program history, having led the Gamecocks to a 27-5 record as a starter.
“I'm just going to go play,” Shaw said on Friday. “With my capability and my style of play, nothing's going to change. I'm not in garnet and black anymore. I'm in white and brown and orange. It's football at the end of the day.”
Manziel was placed on injured reserve after suffering a hamstring injury in a loss last week to the Carolina Panthers, while Hoyer reportedly is listed as doubtful as he deals with shoulder and biceps injuries.
The Browns (7-8) are in last place in the AFC North.