The 30-year-old's contract was due to expire next year.
The former Waikato Chiefs and Llanelli Scarlets forward moved to the Scottish capital a year ago, but he has been out of action in recent weeks with a rib injury.
Meanwhile, a scan has revealed that Duley's fellow Kiwi Matt Mustchin has not suffered a fracture to his shoulder.
The flanker was injured during Edinburgh's Magners League triumph over Llanelli on Friday.
However, the 29-year-old has suffered severe bone bruising along with soft tissue disruption.
A statement from the club said: "He has commenced his rehabilitation programme and will progress as pain allows."
Chris Paterson will have treatment throughout this week after sustaining some soft tissue damage to his back at Murrayfield last Friday evening.
But he should be available for selection for Saturday's Heineken Cup match against Leinster at Donnybrook.