The veterans have set off from the Canary Islands.
They aim to row the 3,000 miles in under 55 days as part of the Talisker Whisky Atlantic Challenge.
The Row2Recovery group are competing against 25 other teams in the race, which will end in Antigua in the Caribbean.
The race was scheduled to start on 15 December, but stormy weather postponed the challenge.
One of the rowers, Lee Spencer, said: "We'll literally be on our own.
"We have a life raft and personal location devices and if we end up in the water swimming is not a big deal. We only have three legs between us.
"But the day-to-day chores are the things we'll struggle with."
Mr Spencer said they had been training their upper bodies to compensate for having lost lower limbs.
"We want to be an example to all people; we're just normal guys who have suffered some misfortune, but life carries on," he said.
Cayle Royce - 29, from Dartmouth. Suffered serious injuries serving in Afghanistan
Paddy Gallagher - 30, from Cambridgeshire. He was injured in Afghanistan while serving with the Irish Guards
Nigel Rogof - 56, from Hereford, who lost his leg while taking part in an RAF parachuting display
Lee Spencer - 46, from Yelverton in Devon. He lost a leg when he was struck by debris when he stopped to rescue a seriously injured motorist on the M3
Also competing are a group of four women aged 44 to 51 from Yorkshire, and 20-year-old University of Bristol aerospace engineering student Callum Gathercole, who is a solo competitor.
Crews will spend at least a month at sea, living on freeze-dried food, while raising money for charity.
Carsten Heron Olsen, race organiser, said: "This year we have 26 teams from the US, Italy, the UK, Antigua, Australia and South Africa, and there are 62 rowers in total.
"Winds look extremely favourable for the rowers for the first few days at sea, and alongside the high level of professionalism of the participants, we're anticipating a quick and competitive race and hopefully break some records.
"The race was planned to start on Tuesday, but due to strong winds going in the wrong direction we had to delay the race for a few days."

Alex Williams, 22, from Christchurch, had failed to appear in court for sentencing in November, but was arrested in the town on Sunday.
He appeared at Bournemouth Crown Court earlier and was sentenced to 20 months in prison for violent disorder.
Williams was also sentenced to a further two months for failing to appear in court.
Detectives had appealed to the public to help locate him after he failed to show up.
The gang's offences included throwing a liquid, thought to be ammonia, at two victims who were each left blind in one eye.
Four men were jailed for the attacks.
In November Joe Warne, 21, was sentenced to 20 years; Reece Watkins, 22, was sentenced to 18 years; Dominic Barker, 20, was given 16 years and Piers Fox-Havilland was jailed for 12 years.
The men, who lived in the London area, were also sentenced to 12 years for conspiracy to rob and eight for possession of imitation firearms - to run concurrently.
Dorset Police said the gang was charged following a lengthy investigation into attacks at locations including Boscombe and Christchurch.
Four ex-servicemen are rowing across the Atlantic in a bid to become what is believed to be the first all-amputee team to make the trip.
[NEXT_CONCEPT]
A man who was part of a five-strong gang that committed violent acts in Dorset has been jailed.