Cleveland needed an experienced guard after losing Shawn Lauvao and Jason Pinkston to ankle injuries in the past week. Browns coach Rob Chudzinski said Moffitt is a "tough and versatile lineman who will be in the mix for us up front."
The 6-foot-4, 319-pound Moffitt made 15 starts over the past two seasons. He started the final six games four at right guard, two at left last season, helping Seattle earn a spot in the NFC playoffs.
The Seahawks drafted Moffitt in the third round in 2011. He started his first nine games as a rookie before sustaining a season-ending knee injury.
Sanford played in six games the past three seasons for Cleveland.