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.
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