The move looked likely to fall through when the stand-off, who has been
plagued by injury, was last month refused an endorsement to play in England.
But the club successfully appealed the RFU's decision and signed him to a three-year contract.
"We are very much looking forward to Stephen joining us here at Bath," said Bath director of rugby Sir Ian McGeechan.
"He is a very effective, skilful player, with a lot of experience which will prove highly beneficial to the younger members of our squad and academy.
"Players he has played alongside all speak very highly of his ability and in particular his character, and we expect him to fit in very well here at Bath, having a hugely positive influence on the squad on and off the pitch."
An RFU spokesman said of the appeal: "The panel accepted that Stephen Donald is an internationally established player of the highest calibre who can play an important role in the development of the game at the top level in this country."
Donald, 27, can now apply to the UK Border Agency for a visa.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.