Hooper will move from Headingley on a three-year deal this summer.
Harrison played 34 Tests for Australia after making his debut against the British Lions in 2001 and he started the 2003 World Cup final defeat to England.
The 33-year-old captained Ulster to the Magners League title in 2006 and Bath coach Steve Meehan believes Harrison will prove an inspirational signing.
"Justin has considerable experience of rugby at the very highest level, both internationally with the Wallabies and in the Super 12 with the ACT Brumbies and in the Heineken Cup with Ulster," said Meehan.
"A natural leader on the park, Justin's qualities fit in perfectly with the ambitions of the club and will assist in raising existing performance standards.
"I believe Justin will enhance the development of younger locks from the Academy and bring a competitive winning attitude that less experienced players can really learn from."
Bath, who are also losing England centre Olly Barkley to Gloucester this summer, are currently third in the Guinness Premiership table and challenging for their first league title since 1996.
"Joining Bath presents a fantastic opportunity to become part of a team that represents the true professionalism and competitiveness that is required to successfully challenge in the Guinness Premiership and in Europe," said Harrison.
"The team is producing an exciting and innovative brand of rugby which is made possible by the dynamic quality of the players.
"Importantly, the squad also has a balance of youth and experience that has presented me with an opportunity to become part of a top Premiership team."