ESPN’s Adam Schefter reported the signing first.
The Bears were interested in replacing O’Donnell with nine-year veteran Kevin Huber, but the unrestricted free agent re-signed with the Bengals a day earlier for $7.95 million over three years.
O’Donnell was also a free agent and had drawn some interest from the Eagles and Giants, both of whom have vacancies at punter. But he decided to return to the Bears, where he has punted since the Bears drafted him in the sixth round in 2014 out of Miami.
O’Donnell has frequently displayed a strong leg but has had an uneven career.