Richard Baker, 65, was a petty officer on the aircraft carrier HMAS Melbourne when it collided with the destroyer HMAS Voyager during exercises off the New South Wales coast in 1964, killing 82 men.
The government offered a 300,000-dollar (213,000 US) compensation settlement in the Victoria state Supreme Court after hearing evidence that Baker has only six months to live.
The court heard Baker was ordered not to discuss the accident with anyone, including family members, and suffered post-traumatic stress disorder.
Baker's legal team said he changed from an ambitious officer to an anxious, depressed man who quit the navy in 1966 and coped with his problems by drinking and smoking heavily.
The government set up a compensation scheme for survivors from the Voyager in 1995 but continues to contest claims made by survivors from the Melbourne.
Solicitor David Forster, who has acted for more than 120 crew members involved in the accident, accused the government of dragging its feet on compensation for the crew of the Melbourne.
About 70 cases have been settled, but there are still about 125 outstanding.
"The government is deliberately seeking to prolong these cases for another 10 years in the belief that the crew members will die before obtaining justice," Forster said.
Baker told reporters outside the court he was relieved the marathon case was over and he hoped his victory would pave the way for other survivors to win compensation.
"It's been a long process and I'm just glad it is all over," he said.