The former policeman began on Sunday morning, setting off from a beach in the Senegalese capital Dakar, and managed nine miles in nearly seven hours on the first day.
Afterwards, his support team wrote on the expedition's Facebook page: "A great start to an epic adventure."
His website, Swimthebigblue.com, says Mr Hooper aims to swim up to 10 hours a day in two sessions, for about 140 days.
This will allow him to cover the straight line distance of 1,879 miles to the Brazilian town of Natal, even though the support boat he will sleep on is expected to travel about 3,500 miles due to it drifting on the ocean's currents.
The website says the 38-year-old will eat every 20 to 30 minutes by being thrown food or taking it off the end of a pole, in order to consume the 12,000 calories a day he needs.
Extensive logs will be taken of his progress, using GPS tracking and video evidence, to make sure he complies with recommendations set by the World Open Water Swimming Association.
In order to deter sharks, he will wear a shark repulsion device and his support boat will be fitted with more sophisticated equipment.
Mr Hooper, who has undergone training in Florida and the Mediterranean for his challenge, aims to raise £1m for charities.
The website says the sea will range from 26C to 34C and there will be strong equatorial currents pulling him west and northwest.
It says: "His epic swim will take him over 30-foot swells, passing through shark inhabited regions, and without doubt, he will encounter jelly fish, flying fish and a harsh equatorial sun.
"When successful, Ben will be the first man in history to have swum an ocean in full, every single mile of The Atlantic Ocean, and will be the first man to explicitly and transparently detail his swim."
A Frenchman, Benoit Lecomte, swam from Massachusetts in the US to Quiberon in northwest France in 1998 but did not make the record books because he was forced to rest up in the Azores for a week.
Another man, Guy Delage, claimed to have swum the ocean in 1994 but was not supervised and did so with the assistance of a flotation aid.