The Australian, 38, is the oldest man to compete in Super League and includes spells at Wakefield and York during his 14-year playing career in English rugby league.
He said: "I have always been interested in rugby union and always followed it closely. When an opportunity came to join a club like Bath it was one that I could not refuse.
"I'm really pleased that I've made the move. First and foremost it is about adding something to the club.
"Hopefully my years of experience in rugby league, especially in defence, will help the club's ambition to be at the top of European rugby."
Bath's acting head coach Steve Meehan has been impressed by the speed of Davis transition to union.
"We are very happy to have Brad on board - he's made an immediate impact," he said.