"This is the outcome we have been working towards since the emergency beacon was activated on Wednesday afternoon.
"It is the result of an excellent coordinated effort involving the RNZAF, which provided a link for the two people on the Windigo when there was no other means of contact, and the Navy, and I would also like to express my appreciation to the captain of the Chengtu and the crew of the Adventure Bound for their efforts."
The pair's medical conditions will be assessed aboard the Chengtu, which is heading south to meet Navy vessel HMNZS Otago late this afternoon.
Earlier, the couple were said to be "tired and scared" on their damaged yacht Windigo, which was sinking 1260km from New Zealand.
Rescuers were racing to save the pair after their sinking yacht rolled in 10m seas off Tonga during a home-coming voyage to Auckland.
Davies, 43, and Jones, 52, were still facing high seas and 75km/h winds last night on board their severely damaged 11.6m yacht, Windigo.
"They're very tired and obviously pretty scared," senior search and rescue officer Keith Allen of the Rescue Co-ordination Centre said late yesterday.
"We've spoken to family in the UK and the Auckland region and ... obviously they fear what's happening but also [feel] relief something is being done."
Ms Davies and Mr Jones wrote posts on their Facebook page last month about being in Tonga, and spoke to friends of their plans to travel to Auckland.
"Yippee in Tonga," they said in a post on October 16.
On October 31, they wrote a post to a friend: "See you soon in Akl."
The friend replied: "Safe journey on your final stage."
Yesterday, a friend posted on their Facebook page: "Praying for you Steve and Tanya [sic], stay strong xx."