The three-year, $18 million deal was first reported by NFL Network.
Uzomah was among several signings the Bengals worked out on the first day of the NFL's open negotiating window. The Bengals also will re-sign right tackle Bobby Hart, who is expected to sign a three-year deal worth $21 million, as reported by ESPN's Adam Schefter.
Uzomah, a 2015 fifth-round draft pick out of Auburn, started 15 games for Cincinnati last season. He became the primary tight end after Tyler Eifert and Tyler Kroft went down with injuries. Eifert, who broke his ankle in September, is still a free agent, while Kroft is expected to sign a three-year deal with the Buffalo Bills.
Uzomah had a career-best 43 receptions for 439 yards and three touchdowns in 2018. He played all 16 games despite injuring his shoulder in the second game of the season. He was essentially the only healthy tight end due to a rash of injuries at the position.
Hart signed a one-year deal with the Bengals last season after spending the first three years of his career with the New York Giants. He was released by the Giants on Feb. 9, 2018, after an ugly ending to his stint there. Hart was accused of refusing to play in the final game of the season, a claim he denied after signing with the Bengals a few days later.
Hart started all 16 games at right tackle for Cincinnati but led the team with 14 penalties.