The 33-year-old Davies continued sailing to Elies until event organisers gave her the green light to resume racing. She finally returned to the route, continuing towards the next racing mark, at 1030 GMT, said the organisers.
Davies, a Cambridge engineering graduate from Hamble, Hampshire, told the BBC she had received a call from HMAS Arunta to say that Elies was safely on board.
"His spirits are good and everything has finished happily, which is a big relief to me," she said.
"It really is a dangerous race... and we must take care out here."
Yann Elies and his fellow competitors set off on 9 November
Speaking to BBC News Channel from her boat she later said her role in aiding Elies would have been mainly to provide a "morale boost", and to let him know they would not leave him alone until the navy arrived.
"It is very important help, psychologically," she added.
Mr Hocken added: "Sam is an example of the great bonds of friendship and assistance that this class enjoys here."
Guillemot and Davies, who took a 40-hour diversion to reach Elies, will receive time credits and will not lose their positions in the race.
Organisers said an independent international jury would make a decision in the next five to 10 days as to what their positions would have been had they not gone to Elies's aid.
Elies was also complaining of chest pains and was confined to his bunk after the accident. A member of his team said his mood improved after making radio contact with Guillemot.
His thighbone was broken when a massive wave slammed into his boat as he was changing a sail on Thursday.
He managed to drag himself into the cabin and activate the vessel's autopilot.
The Frenchman's team says they will attempt recover the yacht, which is currently about 800 miles (1,287km) off Australia's southern coast.
Samantha Davies on her attempt to rescue Yann Elies
This is not the first time Australian forces have rescued Vendee Globe racers. They went to the aid of Briton Tony Bullimore and Frenchman Thierry Dubois in the 1996-97 race.
The rescues drew criticism because of the cost to the Australian taxpayer, but Vice Admiral Russ Crane said the navy had no hesitation in responding to the request to help Elies.
"They are very experienced and diligent operators and no one knows the conditions in the Southern Ocean better than they do," said race director Denis Horeau.
Thirty yachts began the race, held every four years, from the French Atlantic port of Les Sables d'Olonne on 9 November, but 12 have now withdrawn.
Foncia skipper Michel Desjoyeaux is in the lead as the racers approach the southern Pacific Ocean.
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