Jake Browning has been the Bengals' number two quarterback the past two seasons and has played in 12 games, including seven starts in 2023 after Burrow suffered a season-ending wrist injury.
Logan Woodside was waived to make room for Ridder.
Cincinnati also announced the signings of defensive tackles McTelvin Agim and Taven Bryan, along with center Andrew Raym.
The defensive line signings are likely to provide depth after first-round pick Shemar Stewart did not report with the rest of the rookies on Saturday, and Trey Hendrickson, last year's NFL sack leader, expected to hold out as he seeks a new contract.
Veterans report on Tuesday, with the first practice scheduled for Wednesday.
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