Denton, 25, joins from Edinburgh, subject to a medical.
Bath had been thwarted in their bid to sign Wales number eight Toby Faletau from Newport and lost the code-switching Burgess last week when he returned to Australia's South Sydney Rabbitohs.
Burgess, who joined Bath last year, was a surprise inclusion in England's 2015 World Cup squad and, despite playing at flanker for his club, was utilised as a centre by coach Stuart Lancaster.
He was criticised for his performances during the rugby union tournament and British media immediately began reporting that he was considering a return to the 13-man code.
Zimbabwe-born Denton, who can switch between blindside and number eight, has won 32 Scotland caps.
"We've been looking to bolster our back row for some time now so we're very excited that David is joining us," said Bath head coach Mike Ford in a statement.
"He had an excellent World Cup especially in the quarter-final when he managed to outshine one of the best Australian back rows I’ve seen for a long time. He's going to fit in very well with the team and the way we play here."
(Reporting by Justin Palmer; Editing by Tony Jimenez)
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