Cundiff, 35, signed on with the Cowboys as an undrafted free agent out of Drake back in 2005. Since then Cundiff has played for several teams including the Buccaneers, Packers, Saints, Falcons, Chiefs, Lions, Ravens, Redskins, 49ers, Jets and most recently for the Browns.
The Bills signed him to a contract for their Week 5 game, but he was released shortly after.
In 2014, Cundiff converted 22 of 29 field goal attempts this season, but was just one of three from 50 yards or more.
Bullock, 25, was in the final year of his four-year, $2.278 million contract when the Texans elected to release him a few weeks ago and sign former Chargers K Nick Novak.
He recently tried out for the Jaguars, but didn’t receive an offer from the team.
Bullock has converted 83.3 percent of his field goals this season over the course of three games, but has missed two of his five extra point attempts.