The 23-year-old, who will join from Valence d'Agen, has been an ever-present for his international side since 2008 and scored a try against England at last year's World Cup.
Basilaia said: "It's a great honour and opportunity for me to join such a high profile club and I'm really looking forward to being part of a very exciting future and playing alongside some very talented players."
He continued: "The arrival of a new player always heightens supporters' enthusiasm and anticipation and I will not spare any efforts to meet those expectations from the moment I arrive in the capital.
"I'm in great shape, both physically and spiritually, and can't wait to pull on the black and red shirt of Edinburgh Rugby."
Head coach Michael Bradley worked with the player during his spell as technical coach of the Georgian team.
"I believe that Dimitri will prove to be a very significant signing for Edinburgh Rugby," Bradley said.
"He's a fantastic fit for this club and will contribute a huge amount to an increasingly aggressive and combative forward unit at Edinburgh Rugby, while his ball handling skills are such that we can maintain and strengthen our fast-paced, offloading game.
"Dima has a tremendous work ethic and attitude to the sport."