The British Divers Marine Life Rescue said the giant mammal died at about 8pm.
Experts had been attempting to save the animal after it was found on Hunstanton beach on Thursday morning, but resorted to comforting the whale after it became obvious a rescue was impossible.
The whale was breathing but not moving when the water rose over it, a spokesperson for the British Divers Marine Life Rescue told The Huffington Post UK.
It is thought that the animal's muscles started releasing toxins that could cause organ failure.
Before the tide rose, people were pouring water over it to keep it comfortable. British Divers Marine Life Rescue said it was no longer trying to keep the 14-metre long whale alive because it was too heavy to move and already close to dying.
It is expected to "expire in the course of the next 24 hrs" according to the operation's investigation manager.
The rescuers told The Huffington Post UK they would have to "let nature take its course".
There were hopes the rising water could help to free the animal which is estimated to weigh at least 25 tonnes but a reporter at the scene said she didn't think it "stood much of a chance".
A spokesperson for British Divers Marine Life Rescue told the Huffington Post UK earlier in the day: "We can't do anything for it because it weighs between 25 and 35 tonnes so it is a very big whale.
"The tide is on its way in so something may happen with that, but we have to let nature take its course."
The animal was about 1.5 miles out on the sand and the coastguard was helping with the operation, British Divers Marine Life Rescue said.
BBC Radio Norfolk journalist Jill Bennett was at the scene and said the whale was alive and breathing.
She told the station earlier on Thursday: "I'm standing on the beach between Old Hunstanton and Holme, about 50 yards (45m) away from the whale.
"It's still alive and bedded well down into the sand. Coastguards and other agencies are putting water over it to keep it comfortable and stop its skin from drying out."
"From time to time the whale is moving its tail. It's a very sad sight," said Bennett. "I have been speaking to Kieran Copeland from the Hunstanton Sea Life Sanctuary and he said unfortunately the situation does not look good."
In January, five sperm whales became stranded and died on beaches in Hunstanton and Skegness.