The deal is for one-year, $1.02 million, a source told ESPN NFL Insider Adam Schefter.
Cundiff, who originally signed with the Browns last September, was set to become an unrestricted free agent Tuesday.
Cundiff, 33, was solid in his second stint with Cleveland last season, making 21 of 26 field goal attempts. His 80.8 percent success rate was his highest since his Pro Bowl year with Baltimore in 2010.
Entering his 11th season, Cundiff also has played for Dallas, New Orleans and Washington in his career.