The Exeter-headquartered firm said the appointment would add a litigation presence to its commercial property practice in Bristol.
"We're looking to expand into new areas and Andrew brings litigation experience to the commercial property team," said Bristol managing partner Garry Mackay.
"We're looking to expand into new areas and we don't have a presence in commercial property in Bristol," said Bristol managing partner Garry Mackay.
Baines's clients include Bristol & West, Halifax and Royal Bank of Scotland.
Since opening the Bristol office in 2006 Ashfords has expanded from a team of three to 40, with six partners now in place.
Mackay added that the firm will now look to build up its commercial litigation practice with a lateral hire.
A Burges Salmon spokeswoman said: "We're very sad to lose Andrew and wish him the best of luck with his career."
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