A Browns spokesman said the team wouldn't announce any moves Thursday night. The players' agents didn't immediately return messages left by The Associated Press.
Wallace, a career backup in the NFL, was 1-3 last season after replacing starter Jake Delhomme, who injured his ankle during the season opener. Wallace then was sidelined after suffering a similar ankle injury Oct. 10.
Wallace recently said he wanted to compete for a starting job, and when the Browns indicated that Colt McCoy likely would be their No. 1 quarterback next season, it was assumed the former Seattle Seahawk would sign elsewhere. But Wallace is familiar with the West Coast offense that new Browns coach Pat Shurmur plans to install, and the team wanted him back.
Jackson signed a one-year deal worth up to $4.5 million, The Plain Dealer reported, citing a league source. The newspaper also pointed out that general manager Tom Heckert said last weekend at the NFL Scouting Combine that Jackson's size will make him a better fit as Cleveland switches to a 4-3 scheme.
Jackson has missed most of the past two seasons with two torn chest muscles that required surgery. His durability issues explain the nature of his new contract, which is loaded with incentives based on playing time and production.
"I'm backk!!" Jackson wrote on his Twitter page. "It's been a long time browns fans. Thanks to everyone I can assure you I won't let you down!!"
The Associated Press contributed to this report.