Louw, 25, has signed a two-year-deal and effectively replaces outgoing captain and fellow Springbok Luke Watson who is returning to SA to play for the Kings.
Louw is expected to be part of the South Africa squad for the Rugby World Cup squad and if selected will arrive at the Rec in December.
However, should he miss out of selection, Bath could welcome him as early as September.
Bath still intend to find a replacement for Springbok flyhalf Butch James who quit the club and returned to SA where he will play for the Lions.
Louw has seven Test caps to his name since making his debut against Wales at the Millennium Stadium in June 2010.
Louw will start for the Stormers in their Super Rugby clash against the Sharks in Cape Town on Saturday.
(BBC Radio Bristol & News24)