The ICC had proposed that a three-man tribunal, sitting in Zimbabwe, resolve the dispute that has plagued Zimbabwe cricket for several months, an offer already accepted by the ZCU.
Most of the rebel players are currently on a charity tour of England and their manager Clive Field said: "We had a meeting yesterday (Wednesday) and we sent an e-mail to ICC chief executive Malcolm Speed, who is in India, saying we accepted the plan.
"From the players point of view we want this resolved as quickly as possible," Field added.
"We don't know when the arbitration will start but we hope the composition of the panel and their terms of reference can be decided quickly."
The ICC had set the rebels a deadline till Thursday (2130 IST) to accept their proposal after the players initially asked a week ago for a further month in which to make up their minds.
Last Wednesday the ZCU agreed to the ICC's plan for a three-man tribunal, sitting in Zimbabwe, which would aim to end the crisis.
One representative would be appointed by the ZCU and another by the players with both those people choosing the third, the chairman.