He started his 2,000-mile (3,200 km) swim from Dakar harbour in Senegal, west Africa.
Mr Hooper's four-month attempt is due to end in Natal in north-east Brazil, next March.
The 38-year-old long-distance swimmer from Cheltenham is hoping his sponsored Swim The Big Blue challenge will raise £1m for charity.
Other people have attempted the swim, but were not ratified by Guinness World Records.
French swimmer Benoit Lecomte was credited as the first to swim across the Atlantic without a kickboard in 1998, but this was not verified.
Mr Hooper said he faces hazards such as storms and ocean predators.
"The idea is to get across safely and I think my only real fear is if something goes mechanically wrong with me."Beyond that I am not too worried about marine life. I am going into their world, so I need to be respectful," he said.
"I've already met sharks and jellyfish and nothing has eaten me yet."
Mr Hooper is swimming freestyle front crawl for up to 12 hours a day, and will have to eat 12,000 calories a day to maintain his strength.
He is accompanied by two support boats. The crews include a medic, body therapist and an official observer who will be reporting back to Guinness.
Nigel Taylor-Schofield, captain of one of the support vessels, said before the swim: "There are not many 'firsts' left in this world and I am looking forward to helping Ben join that exclusive and elusive club."
Mr Hooper has completed 12 million metres (7,456 miles) of ocean and pool swimming in preparation.