The Great Britain and England rugby league international has agreed a three-year deal to join the Aviva Premiership outfit from NRL side the South Sydney Rabbitohs later this year.
The 25-year-old Yorkshireman will remain with the Rabbitohs for the remainder of the 2014 Australian season before making the switch to Bath and rugby union in October, with the ambition of going on to become a dual international for his country.
Burgess said on the Rabbitohs website: "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.
"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, who has scored seven tries in 13 appearances for England, left Bradford Bulls for the Rabbitohs in 2010 and he had three years left on his contract with the NRL side.
He admitted it was not easy to decide to leave the Rabbitohs but is excited about the next phase of his sporting career.
He said: "This has been a tough decision for me to make, as I've loved my time in Sydney with the Rabbitohs. However, I'm very excited about the challenge that this move offers me.
"Bath are a very ambitious club, who have a talented young squad, brilliant coaches and a world class set-up and ethos, and I can't wait to get my head down and start learning the game."
Bath said that Burgess had turned down "far more lucrative offers from elsewhere" to move to the Recreation Ground.
There were no details in the Bath statement of the financial deal that has been struck to bring Burgess back to England but the Rabbitohs had reportedly been offered a £500,000 transfer fee by the Aviva Premiership side to release the player from his contract.
It is believed the Rabbitohs were officially contacted about the move for the first time last week and were told Bath would pay the compensation to enable him to make the switch at the end of the season.
The Rugby Football Union, with an eye on the 2015 Rugby World Cup, was thought to be willing to part fund a move that would buy Burgess out of the remaining two years of his contract with the Australian side.
There was confusion as to whether any deal would proceed as rival Premiership clubs opposed plans by the RFU to pay a transfer fee to enable Burgess to play for one of their opponents.
However, Bath appear to have now found the money elsewhere after confirming Burgess' signing.
The Rabbitohs also declined to include any figures in their statement, but did say they had first and last option on Burgess if he decided to return to rugby league one day.
The statement said: "The Rabbitohs recently received a request from Burgess for a release from his contract which, after long discussions, has been granted, with the Rabbitohs negotiating an undisclosed release fee.
"The Rabbitohs have also negotiated a clause in the release that the club has first and last offer on Burgess' services should he return to Rugby League in the future."