The news ends weeks of speculation about the English forward's future, with the two clubs reaching a financial settlement believed to be worth about $900,000.
Burgess said he would aim to play for England at the 2015 Rugby World Cup, revealing a long-held ambition to become a dual international.
"I'm happy this has all been sorted out before the start of the season so that I can concentrate on my game and the team without any other things in the way," Burgess said.
"An opportunity presented itself to head back home to England and to pursue a chance to represent my country in two different sports.
"With 2015 being a Rugby World Cup, it was an opportunity I had to pursue and I thank the Rabbitohs for allowing me to make this move and start the next chapter in my sporting career."
Burgess joined the Rabbitohs from Super League club Bradford in 2010, becoming one of the best players in the NRL.
He insisted he would maintain high standards in his final season as the club attempt to win their first premiership since 1971, having reaching the preliminary final in the last two seasons.
"We have a great opportunity in front of us now as a group and I'll be doing my best every week to help us win each game and hopefully improve on what we've been able to achieve in the past two seasons," he said.
"My teammates, coaches, staff and the Rabbitohs members have been a huge support to me over the past four seasons and hopefully I can repay that support in 2014."
The Rabbitohs have negotiated a clause in the release that ensures they have first and last offer on Burgess' services should he return to rugby league in future.
Rabbitohs coach Michael Maguire said he expected Burgess to maintain his form.
"Sam remains completely focused on his job with the Rabbitohs this season," Maguire said.
"Sam has made a real impact on the NRL over the past four seasons and his focus is on his job here at Souths, as we're all focused on our goals for this year."
Burgess has signed a three-year deal with Bath, who are coached by former Great Britain rugby league halfback Mike Ford.
Ford is confident the big Yorkshireman has the qualities to make a successful transition to rugby.
"I've known Sam since his rugby league days in England and he is an exceptionally talented athlete," Ford said.
"He's hard working, a huge presence both on and off the field, and an ambitious young Englishman.
"All of which are qualities that we are building our squad around.
"I've no doubt Sam will fit in seamlessly here at Bath and we're looking forward to having him join us and start making the transition."