"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.
"It pretty much all worked to plan, and we are very excited to have him on board now. It's a great feeling."
The crew expected strong winds and waves of between three and seven meters (10 to 23 feet), and were preparing to approach the raft directly and winch Delord up if they were unable to launch the Zodiac.
The Orion was 11 days into an 18-day passenger cruise of the Antarctic and sub-Antarctic when it was drafted into the rescue. It was the only ship within 100 nautical miles to respond to AMSA's distress call.
AMSA dropped Delord food, water, communications equipment and a safety suit on Saturday and had stayed in regular contact with him up to the rescue.
The experienced yachtsman has been at sea since October last year and was reportedly following the route of the Vendee Globe round-the-world ocean race.
Frenchman Thierry Dubois and Briton Tony Bullimore were famously rescued by the Australian navy after several days adrift in the Southern Ocean during the 1996/97 edition of the Vendee Globe.