The 19-year-old centre moved from his homeland to Edinburgh a year ago, but has struggled to break into the first XV.
He represented his country at age-grade level and joined Edinburgh straight from school in Stellenbosch.
Venter, who is qualified to play for the Springboks and England, has been monitored by Bath for more than a year.
The Gallagher Premiership club expect him to provide cover during international periods when they could potentially lose first-choice centres Cameron Redpath, Max Ojomoh and Jonathan Joseph.
Bath director of rugby Stuart Hooper said: "We actually tried to sign him a year ago but it didn’t work out for various reasons.
"He is English qualified, he is a dynamic young centre who can play on the wing and he is someone we have seen potential in for a long time.
"I always enjoy these signings when you have had a long run at them and a good look,” added Hooper.
"We have met him a couple of times and watched him play a lot and now he has joined us and will be putting his hand up for selection pretty soon I would say.
"It is about making sure we have got a competitive squad for training, so we have competition there and can push each other. He is very ambitious and very hungry and has a lot of the tributes we look for off the field as well."
Edinburgh coach Mike Blair added: “Jordan is a hard-working player with a great attitude, but given the current competition for places in the centre, and Jordan’s ambitions for more game time, we felt it was the right time for him to move on and test himself in another playing environment.
“We wish him the very best moving forward and thank him for his commitment to the jersey during his time in Edinburgh.”
Venter’s departure means that Edinburgh have Mark Bennett, Chris Dean, Cammy Hutchison, Henry Immelman, James Johnstone, James Lang and George Taylor to choose from at the centre position.