"Andy will always hold a special place with this franchise, and I know that he holds a special place in my heart," Bengals owner Mike Brown said in a news release.
"This is a hard day for our club because we know and appreciate what a consummate professional Andy has always been. We respect and appreciate Andy, and we thank him," Brown said.
Sources told NFL Network and ESPN that Dalton asked for his release. The move came a week after the franchise selected former LSU quarterback Joe Burrow with the No. 1 overall pick in the 2020 NFL Draft.
"Andy will always be considered a key member of the Bengals' organization," Bengals coach Zac Taylor said. "His teammates and coaches appreciate his leadership and his commitment to winning.
"Just as importantly, Andy and his wife J.J. are leaving a lasting impact in the community with the incredible work their foundation has done over the years. Andy and his family have meant a lot to this team and this city, and we wish them the best in the future."
Dalton, 32, started 13 games last season for the Bengals. He completed 59.5 percent of his throws for 3,494 yards, 16 touchdowns and 14 interceptions. The second-round pick in the 2011 NFL Draft posted a 70-61-2 career record as the Bengals' starting quarterback.
Dalton completed 62 percent of his throws for 31,594 yards and a franchise-record 204 touchdown passes in Cincinnati. His 70 wins rank second in franchise history. Dalton won 50 games as a starter in his first five seasons with the Bengals.
The TCU product was set to earn $17.7 million in 2020, the final year of his six-year, $96 million contract.