Their new home will be in the Eritrean highlands, bringing to an end a huge animal rights campaign which began shortly after they left the Australian port of Fremantle on 5 August.
The plight of the sheep - 5000 of which died aboard the vessel Cormo Express - caused a political storm in Australia where the government faced calls for a ban on its lucrative live animal export trade.
"They began getting off the boat this morning," said an employee of the Red Sea port of Massawa. "They are taking them to Ghatelei," in the highlands of the east African country.
Crew members said the Cormo Express had arrived in Massawa on Wednesday morning.
The vessel, dubbed the Ship of Death, had been sailing around the Middle East since Saudi Arabia rejected the sheep in August, claiming they were diseased.
"We certainly will be doing everything we can to ensure this circumstance never arises again"
Australian Trade Minister
Independent veterinary surgeons said there was nothing wrong with them, but about 30 countries followed the Saudi lead and refused to take them.
Dr Nigel Brown, a veterinarian with Meat Livestock Australia (MLA) for the Middle East and Africa region, said Friday the animals had been inspected by Eritrean veterinary authorities before they left the ship and they were in good health.
"They are showing no signs of clinical disease, of infectious disease or contagious disease," he told reporters.
"They are very fit and healthy and we are delighted. They will be looked after well in Eritrea where there are excellent facilities."
Earlier Friday, Australia announced that the sheep had been given as a "gift" to Eritrea. Brown said the Australian and Eritrean governments had "reached an agreement that is mutually satisfactory."
In the afternoon, the main road out of Massawa was crowded with sheep and their shepherds.
Authorities barred access to the port but the smell of the sheep was detectable well outside the facility.
The port worker, who had been aboard the Cormo Express, said he had not seen any dead sheep.
Australian Trade Minister Mark Vaile said the fiasco would never be repeated.
"We've managed it the best way we can and we certainly will be doing everything we can to ensure this circumstance never arises again," Vaile said.
Vaile conceded that negotiations over the sheep had been sensitive.
Australia's agriculture industry had been deeply concerned by government plans to return the sheep to Australia for slaughter if a taker could not be found, fearing the animals could be carrying exotic diseases contracted during their lengthy voyage.
Animal rights activists had been calling for the animals to be slaughtered at sea and suggested the unexpected deal with Eritrea had been kept secret to minimise a bad press and prevent independent scrutiny of the animals' condition.
Previously the government said they had left Kuwait en route for the Cocos Islands, an Australian possession in the Indian Ocean where there is a quarantine station, travelling in the opposite direction to Eritrea.
"I would suggest that the timing of the announcement was cleverly orchestrated to ensure that media scrutiny of the condition of the sheep was avoided"
"Animals Australia welcomes an end to the Cormo Express debacle," said Glenys Oogjes, the rights organisation's executive director: "However, I would suggest that the timing of the announcement was cleverly orchestrated to ensure that media scrutiny of the condition of the sheep was avoided."
The Australian government has paid dearly for the debacle. Live exports to Saudi Arabia have been halted and the government was forced to repurchase the sheep at a cost of several million dollars.
The Labour opposition has been scoring political points over the issue with an eye on an election due next year.