The 26-year-old made three appearances for Bath after joining in January, having previously played for London Welsh and Harlequins.
Though born in London, Marfo qualifies to play for Scotland through his Ayrshire-born mother.
"I'm massively excited to be joining Edinburgh. It seems to be a really exciting time at the club," he said.
"The Edinburgh front row is talked about in such high regard in rugby circles, so it's great to have the opportunity to be around those guys. Hopefully I can contribute towards making that unit stronger.
"I can't wait to get cracking."
Head coach Richard Cockerill described Marfo as "a big, powerful scrummager and carrier of the ball".
"He has plenty of promise, and we look forward to seeing him compete for a spot in the coming season," he added.
Marfo will compete for the number one jersey with three Scotland internationals - Alasdair Dickinson, Allan Dell and Rory Sutherland.
Edinburgh have signed loose-head prop Darryl Marfo from English Premiership side Bath on a one-year deal.