Ben Hooper 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 Â£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.

Judge Carlos Castro Martins reversed the order he had issued in September, which had barred any work on the Belo Monte dam that interfered with the natural flow of the Xingu river.
He said the company behind the project had subsequently shown its work would not harm local fishing.
The project has been heavily criticised by environmentalists.
Judge Martins had originally ruled in favour of a fisheries group which argued that the dam would affect local fish stocks and could harm indigenous families who make a living from fishing.
He had barred the Norte Energia company behind the project from all work which could interfere with the natural flow of the Xingu river, including building a port, using explosives, installing dikes and building canals.
Legal wrangling
Norte Energia appealed against the decision and Judge Martins ruled on Friday that construction work on the dam could go ahead as the company had shown that local fishing boats would not be blocked or hindered in their work.
"Since the course of the water won't be altered, and there won't be much variation in the speed of its flow, (the project) won't have a major influence on the habitat of ornamental fish species used for fishing," he said.
Judge Martins did, however, say that the wider environmental impact of the project "could only be felt and analysed once the work was completed, as the studies into its effects were only forecasts of what could happen".
He also said that any work would have to comply with the regulations laid down by Brazil's Indian Affairs Department (Funai) and the National Environment Agency, Ibama.
Norte Energia said the temporary halt on the building work had not affected the project, as it had not yet reached the stage where the company needed to do any of the specific type of work which had fallen under the ban.
If it goes ahead, the 11,000-megawatt dam will be the third biggest in the world - after the Three Gorges in China and Itaipu, which is jointly run by Brazil and Paraguay.
The government says it is crucial to meeting growing energy needs, but environmentalists and those fighting for indigenous rights have been vociferous in their opposition.
A man has set off in a bid to set the first official world record for swimming across the Atlantic Ocean.
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A judge in Brazil has revoked a decision which had halted work on the Belo Monte dam in the Amazon region.