The Browns had been in the market for a kicker after making the surprising decision over the weekend to terminate the contract of veteran Shayne Graham and releasing rookie Brandon Bogotay ahead of Sunday's opener against Miami. Dependable veteran Phil Dawson wasn't re-signed after last season.
Dan Carpenter, a former Pro Bowl kicker with the Dolphins, had been scheduled to kick for the Browns. But a person familiar with negotiations told The Associated Press on Monday night that Carpenter was on his way to Buffalo to try out for the Bills after rookie Dustin Hopkins was injured in practice.
Cundiff, 33, was with the Browns in 2009, filling in while Dawson was sidelined with a strained calf. Cundiff kicked the winning field goal as the Browns beat Buffalo 6-3 in Week 5. Cundiff, a Pro Bowl selection in 2010 with Baltimore, was cut by the Jets this summer.
Cundiff is perhaps best remembered for missing a 32-yarder for the Ravens that would have tied New England in the closing seconds of the 2012 AFC Championship Game.
The Browns have been looking for a kicker since deciding not to re-sign Dawson, who left after his 14th season with Cleveland and signed as a free agent with San Francisco.
It was assumed Graham would be his replacement after the Browns signed the 35-year-old in April. Graham, who spent last season with Houston, went 3 for 3 during the exhibition season but missed the preseason finale with a sore back.
Information from The Associated Press was used in this report.