The cornerback had attracted interest from the Oakland Raiders, but has agreed to a two-year deal with the AFC North side, which he is due to sign in the coming days.
The 34-year-old tweeted: "After much time and thought, I'm heading back to Cincy. And for those of you who think it was about money, the Raiders offered more.
"I came in with [Bengals' defensive coordinator] Mike Zimmer and feel its only right that I leave as him coaching me. Thanks to Raiders Nation for showing me such love."
Newman recorded two interceptions and a forced fumble for the Bengals in 2012.