Bell was the Pirates' hitting coach last season, when they beat the Reds in a one-game wild card playoff. He was the bench coach for Bob Melvin in Arizona for five years.
The Reds also hired Don Long as their hitting coach Wednesday. Long spent the last three seasons with Atlanta as a minor league hitting co-ordinator. He also spent three years as the Pirates' hitting coach.
Jeff Pico will fill Price's spot as pitching coach. Pico spent 11 seasons with Arizona.
The staff includes bullpen coach Mack Jenkins, first base coach Billy Hatcher, third base coach Steve Smith, catching coach Mike Stefanski and Freddie Benavides, who will focus on the infield.