The coastguard received a radio call from a support vessel at about 21:20 BST on Monday.
The search and rescue helicopter based at Lydd, which was training nearby, arrived within 10 minutes and airlifted the swimmer to William Harvey Hospital in Ashford, but he later died.
Mr Waymark's sister, Jo Ikel, posted a tribute to him on Facebook saying: "For all those following the recent updates, Douglas Waymark has not completed his Channel swim.
"Last night he felt he could no longer continue his quest and swam to the boat supporting him. He passed out and was taken by helicopter to a hospital in Ashford. At around midnight, he sadly died.
"We are all devastated but take comfort in him doing what he loved best to the very end."
Mr Waymark was taking part in the Enduroman Arch 2 Arc challenge, a continuous triathlon from Marble Arch in London to the Arc de Triomphe in Paris.
It involves an 87-mile run to Dover, swimming the channel and cycling 182 miles to the French capital.
Mr Waymark had been roughly half way through his crossing attempt when, according to Kent Police, he "became unwell".
After setting off from Shakespeare beach at 07:27 BST he got off to a positive start but began to struggle later in the day.
Updating followers on Mr Waymark's progress throughout, Enduroman tweeted he was given painkillers around 17:00 BST and was "finding the salt a bit harsh".
Swimming across the tide, he missed a feed and Enduroman said "he doubts but pushes on".
The last word on his progress came at 20:30 BST, saying he was swimming on through cooling temperatures and fading light.
Mr Waymark's tracker regularly posted his position online and the last data visible between 21:09 and 21:38 BST showed he had turned around and was heading back towards Dover.
Family and friends posted to social media when they could see no more, asking Enduroman for updates assuming he had been brought to shore on the support boat.
Enduroman has not yet responded to a request for comment.
Kent Police confirmed his death is not being treated as suspicious.