There were "scant" early details of the rescue but AMSA said Delord had been recovered "safely and without injury".
"He is currently receiving medical attention and early indications are that he is healthy," the authority said. "Weather conditions were better than expected and there was plenty of light in the area."
A Fairfax newspaper reporter on board the Orion said Delord had been recovered by a Zodiac inflatable dinghy. He looked "awake and relatively well" as he boarded the ship by a side door to cheers and whistles from those on board.
"He is very tired and being attended to by the ship's doctor," said Ian Vella, manager of the ship's hotel.
"He is very hungry, so he is going to have something to eat and a glass of red wine for his dinner."
Orion tour leader Don McIntyre said it had been an incredibly quick operation.
"(The Zodiac crew) rocketed across the water, grabbed Alain and brought him onto the Zodiac," McIntyre told Fairfax.
"They then rocketed back to us, we brought him up and it was over that quick.