Louw will join the club on a three-year deal after the World Cup in November.
The 26-year-old has been part of the Stormers' side in Super Rugby for the past two seasons but will now move to England to play in the Aviva Premiership.
The deal, which sees Louw come into the squad for the recently-departed Luke Watson, had originally hit the headlines towards the end of last season but it was only completed on Tuesday.
He said: "I am very excited to be joining a side with such a prestigious past and exciting future as Bath.
"I'm looking forward to working hard and competing for a place in the team, in what is a very competitive squad, and helping Bath to become a real force, both in domestic and European competitions."
Louw has scored two tries in seven appearances for the Springboks and added he was "hopeful" of representing his country in the Tri-Nations tournament, which starts later this month, and the World Cup.
Bath's director of rugby Sir Ian McGeechan said: "Francois is an outstanding player and character who will add to, and complement, the squad at Bath.
"We are all very impressed with his qualities and are looking forward to working closely with him."
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