Hooper, 34, retired from playing in April after 138 Premiership appearances for Bath, following spells at Saracens and Yorkshire Carnegie.
He had already been confirmed as a member of new director of rugby Todd Blackadder's backroom team.
Rock, 31, was previously Championship Yorkshire Carnegie's academy director.
Former captain Stuart Hooper has been named as Bath performance and player development director, with Andy Rock joining the club as academy manager.