The 25-year-old, who also plays on the wing, becomes the latest powerful addition to the club's back three, joining fellow internationals Tim Visser and Nikki Walker.
Cuthbert passed a medical last Tuesday and returns to Murrayfield on Monday to begin pre-season preparations with his new club.
He said: "I'm really excited. It's a fresh challenge for me. I'm coming into a completely different environment from Bath where I've spent the past seven or eight years.
"It's a change of league with a very different style of rugby. The Premiership is very much a physical affair while there's a great style of running rugby brandished in the RaboDirect PRO12, with the physicality right up there with the best leagues in Europe.
"This [Murrayfield] is where I made my Scotland debut and I'd love to get the chance to play more Test rugby but I'm only focusing on Edinburgh just now.
"First and foremost I want to make sure I do the simple things well; train hard, get as much game time and do as well as I can for the Edinburgh Rugby."
Cuthbert was selected for Scotland A's 2010 IRB Nations Cup campaign, in which he started all three matches, before being called up to the Scotland squad for the 2011 RBS 6 Nations tournament.
Cuthbert did not make an appearance during the championship but was named in Andy Robinson's provisional 40-man squad for the World Cup and made his Scotland debut off the bench against Ireland in their first World Cup warm-up match in August.
Interim head coach Stevie Scott, said: "It's good to be able to bring another Scotland internationalist to Edinburgh Rugby. Jack's played regularly for Bath in the Premiership and has gained a lot of experience playing in a tough, competitive environment. He's demonstrated a knack for getting over the try-line and is a big, physical player."