Connolly has 20 years of coaching experience to call on, having worked at Queensland, Stade Francais and Swansea and will team up with the current coaching staff of Michael Foley, Brian Smith and Richard Graham.
Director of rugby Jack Rowell said: "John has extensive experience at a very high level.
"As head coach he will lead the coaching role which will include Mike Foley, Brian Smith and Richard Graham as his assistants.
"The goal here is to re-establish Bath Rugby at the top of the Zurich Premiership.
"At the end of last season an in-depth review of the playing side was undertaken.
"This indicated a need to appoint an experienced head coach and John's appointment will allow Foley, Smith and Graham to develop their potential. The review also indicated the need to overhaul the existing playing squad and this is now substantially completed."
Connolly added: "I am extremely excited to be joining this club and am looking forward to this fresh challenge.
"I have been in rugby a long time now and I am fully aware of Bath Rugby's illustrious history and am looking forward to making a solid contribution to the club."