The whale, which was first sighted off Herzliya in central Israel on Saturday, is believed to have travelled thousands of miles from the north Pacific after losing its way in search of food.
"It's an unbelievable event which has been described as one of the most important whale sightings ever," said Dr Aviad Scheinin, chairman of the Israel Marine Mammal Research and Assistance Center which identified the creature.
A population of grey whales once inhabited the north Atlantic but became extinct in the 17th or 18th centuries and has not been seen there since.
The remaining colonies live in the western and eastern sectors of the north Pacific.
"What has amazed the entire marine mammal research community is there haven't been any grey whales in the Atlantic since the 18th century," he said.
Scheinin said the creature, a mature whale measuring some 12 meters (39 feet) and weighing around 20 tons, probably reached the Atlantic through the Northwest Passage, an Arctic sea route that connects the Pacific and Atlantic oceans and is normally covered with ice.
"Here you have an animal that is supposed to live in the Pacific and because the ice in the Arctic is melting, it managed to get through this corridor near the Bering Strait," Scheinin told AFP.
'Happy enough' in waters
The population which lives in the northeastern Pacific normally migrates southwards in around October, heading for warmer waters around the Gulf of California in a huge round trip of at least 5,000 miles (8,000 kilometers).
So when autumn came, this particular grey whale began travelling south, keeping the land mass on the left and heading for the Californian Gulf with the aim of "turning left" into the bay.
But instead, it reached Gibraltar and turned left into the Mediterranean and ended up off the shores of Israel, Scheinin said.
"The question now is: are we going to see the re-colonization of the Atlantic?" he said. "This is very important ecologically because of the change of habitat. It emphasizes the climate change that we are going through."
So far, the whale seems to be happy enough in the waters off the shores of Israel, he said.
"It is pretty thin, which indicates the trip was quite harsh, but we think it can survive here," he said. "Grey whales are very generalist in what they feed on."
Now experts are mulling the possibility of tracking the whale by satellite -- a costly operation that would need outside funding and expertise, Scheinin said.
"It's quite a big operation to do this. If it stays around here for the next month, it's worth having someone come in and do this professionally," he said.
"It will be interesting to see where it goes and to follow it."