The bulk carrier Bardu, escorted by the Italian destroyer Zaffiro, sailed into Djibouti harbour in the early afternoon.
Officials said the Liberian-registered vessel carried five British crew and eight passengers, four South African crew and 35 passengers, seven German passengers, one Dutch crewman and seven passengers, and four Italian crewmen.
Two US navy ships and a merchant vessel carrying passengers and crew from the liner will arrive in Djibouti today. Another rescue ship is heading for Muscat, Oman.
Officials in the Kenyan port of Mombasa said that 604 survivors were due to arrive there today in five ships and would recuperate for a day or two in beachside hotels.
The 977 passengers and crew abandoned the Achille Lauro on Wednesday after a fire in its engine room and were transferred to a flotilla of rescue ships on Thursday about 160km (100 miles) off the Horn of Africa.
Two elderly male passengers died in the tragedy. The Achille Lauro sank on Friday after burning for three days.
Many of the passengers on the liner were elderly. Some suffered broken bones while being transferred to waiting ships across the shark-infested waters off Somalia.
A South African ambulance aircraft arrived in Mombasa on Saturday carrying sun cream, travellers' cheques, tracksuits and toiletries for the survivors, among them 300 South African residents.
British survivor Janice Bell, speaking to BBC Television on Friday from the merchant ship Chios, praised the rescue operation. ``The crew are absolutely unbelievable. They just can't do enough for you,'' she said.
``A lot of people had nightclothes on. They are walking around now in the ship's uniform - boiler suits and things.''
Many of the passengers were sleeping when they were roused to abandon ship and others are in evening dress, having been at a black-tie ball when disaster struck.
The Achille Lauro, which suffered fires and a collision during its 47 years at sea, hit the headlines in 1985 when Palestinian guerrillas hijacked it, killed wheelchair-bound Jewish-American Leon Klinghoffer and dumped his body overboard.