He added the beluga had been feeding around barges on the river for around an hour and had not moved more than 200m either direction on the river.
Photographers line the banks of the Thames to snap the whale.
However rescue teams were on standby in case the animal got into danger.
The whale spotted in the Thames was clearly a mature beluga whale, and possibly a female or a younger whale due to its size, Babey said.
The video has since been viewed more than 160,000 times, sparking "River Thames" to trend on Twitter.
"Hopefully instinct will soon kick in and the beluga will leave the estuary and go out into the north sea and then head north where it should be", the scientist explained.
Danny Groves, from Whale and Dolphin Conservation (WDC) said: "This is a High Arctic species thousands of miles from where it should be in Greenland, Svalbard or the Barents Sea, they are usually associated close to the ice".
"We do have quite a lot of plastic bags, which could be quite an issue", she said.
"We would urge that the whale is given space and disturbance is kept to a minimum".
The rare marine mammal, nicknamed Benny, was seen near Gravesend yesterday and appeared to be swimming strongly and feeding in the estuary.
A spokesaperson said: "We are working with other agencies to monitor the situation and ready to provide appropriate assistance if requested".
A bottle-nosed whale became stranded in the Thames for two days in 2006, but died from convulsions as it was being rescued. They have a rounded forehead and no dorsal fin.
Belugas, which can grow up to 5.5 metres (18 feet) long, spend most of their time off the coasts of Alaska, Canada and Russian Federation, though they often travel great distances in search of food.