A distress call was sent out from the ship around 9 a.m. after the boat started taking on water.
The Ivy Rose, another fishing vessel, was the first to respond to the distress call.
Maj. Martell Thompson, with the Joint Rescue Coordination Centre out of Halifax, said all 19 crew members were able to get off safely before the ship sank.
"That crew was able to make it to a life raft where they were rescued by another fishing vessel in the vicinity, and that fishing vessel is now en route to rendezvous with the George R. Perks Coast Guard vessel," he said.
Thompson said he isn't yet sure where the crew will be taken.
"The crew will be transferred on to the George R. Perks, and a final destination will be determined at that time."
JRCC tasked a Cormorant helicopter out of Gander and a Hercules aircraft from Greenwood, Nova Scotia to assist in the rescue. A Provincial Airlines plane also responded.
The Cape Dorset is owned by Icewater Harvesting out of Arnold's Cove.
The company received $2 million investment from the Newfoundland and Labrador government in April 2013 to help finance the purchase of the ship.