Bullock will replace Matt Prater, who ended up signing a contract with the Cardinals earlier in the week.
Bullock, 31, is a former fifth-round pick of the Texans back in 2012. He spent three years in Houston before signing on with the Jets in 2016.
Bullock had brief stints with the Giants and Steelers before the Bengals claimed him off of waivers during the 2017 season. Cincinnati brought him back on a two-year extension in 2018.
In 2020, Bullock appeared in 12 games for the Bengals and converted 21 of 26 field goal attempts (80.8 percent) to go along with 24 of 25 extra point tries (96 percent).