Deputy Prime Minister John Prescott said the decision had been taken in the light of "new and important evidence" during a survey of the trawler by underwater cameras.
He said it was vital not to jump to conclusions about why the vessel sank, but he hinted that the new information was unlikely to link the tragedy with a Soviet spying mission, as claimed by relatives of the dead, or a storm.
The ship, which was one of the best equipped in the British fishing fleet, sank in 1974 with the loss of 36 lives. Despite a public inquiry shortly after the tragedy, which blamed bad weather, rumours that the ship was sunk because it was involved in spying on Soviet shipping have persisted.
Robot cameras 850ft under the Barents Sea, off Norway, where the ship was lost, transmitted pictures back to Marine Accident Investigation Branch investigators this week. They showed that two hatches and a door were open on the vessel, suggesting an accident.
Mr Prescott said that the chief inspector of marine accidents, Rear Admiral John Lang, had "assured me that his colleagues have found new and important evidence. I therefore intend, once I have received his report, to order a reopening of the formal investigation into the sinking of the Gaul 24 years ago.
"I was delighted to be able to make my intentions known to the relatives of those who died in the tragedy when I met them earlier today. They have campaigned long and hard to find out what really happened to the Gaul and its crew."
Mr Prescott, who is the MP for Hull, where 32 of the victims came from, said: "It would be wrong for any of us to jump to conclusions about the cause of the tragedy before the MAIB inspectors reach their conclusions.
"When their report is published, I hope it will provide the formal investigation with sufficient evidence to put an end to all the rumours of the past 24 years and that we can put the matter to rest."Reuse content