The last in the current group of former US navy ships was docking on Teesside on Wednesday after being delayed by poor light.
The Canisteo arrived earlier this month
The Compass Island has been force to stay off the Teesside coast since 28 November.
It will join three other vessels which have already arrived at the Able UK yard near Hartlepool.
Poor light coupled with unsuitable tidal conditions kept the ship offshore.
But a spokeswoman for Able UK said the vessel was due to dock at 1045 GMT on Wednesday.
The first two ships were met by protesters, who said the fleet was an environmental hazard, containing asbestos and other waste material, and should not have been allowed over from America.
But demonstrators have stayed away since, saying they are now waiting for the outcome of legal challenges.
Able UK won a contract to dismantle and recycle 13 vessels from the outdated US fleet, which had been in the James River in Virginia.
A judicial review is scheduled for the High Court, in London, in December.
It will determine whether the ships can be recycled in Britain or must be returned to America.
The remaining nine vessels which formed Able UK's contract, will stay in Virginia until at least next spring pending legal challenges there.
The first two ships to arrive were the Caloosahatchee and the Canisteo. The third was the Canopus.
Able UK boss Peter Stephenson welcomed the arrival of the ships and said he remained confident that the courts would rule that the work should be carried out on Teesside, creating 200 jobs.
Mr Stephenson, who believes many people have been misled by campaign groups about the safety of the ships, said: "When people know the truth about these
vessels, they will realise there's nothing at all to be worried about.
"I am confident that the work will eventually go ahead here and people should actually be proud of the fact that we secured the contract from America."