The four-seater, called FCX Clarity, runs on electricity produced by combining hydrogen with oxygen, and emits water vapour.
Honda claims the vehicle offers three times better fuel efficiency than a traditional, petrol-powered car.
Honda plans to produce 200 of the cars over the next three years.
One of the biggest obstacles standing in the way of wider adoption of fuel-cell vehicles is the lack of hydrogen fuelling stations.Critics also point out that hydrogen is costly to produce and the most common way to produce hydrogen is still from fossil fuels.
Analysis of the environmental impact of different fuel technologies has shown that the overall carbon dioxide emissions from hydrogen powered cars can be higher than that from petrol or diesel-powered vehicles.
The first five customers are all based in southern California because of the proximity of hydrogen fuelling stations, Honda said.
US actress Jamie Lee Curtis will be among the first to take delivery of the vehicle, the firm added.
The car will initially be available for lease rather than purchase in California, starting in July, and then in Japan later this year.
It is being built on the world's first dedicated production line for fuel-cell vehicles in Japan.
"This is an important day in the history of fuel-cell vehicle technology and a monumental step closer to the day when fuel-cell cars will be part of the mainstream," said John Mendel, executive vice president of American Honda.
Honda says it expects to lease a few dozen units in the US and Japan in 2008, and about 200 units within three years.
It said the cost of the car, on a three-year lease, would be $600 (£300) a month.
The FCX Clarity is based on Honda's first-generation hydrogen fuel-cell vehicle, the FCX concept car. Honda delivered around 34 of these cars, mainly in the US, of which 10 remain in use.
Many car makers are developing cleaner, more economical vehicles because of high fuel prices and as consumers become more concerned with the environment.
Toyota said it was struggling to keep up with booming demand for its hybrid vehicles because it was unable to make enough batteries.
Hybrid vehicles, such as Toyota's top-selling Prius, switch between a petrol engine and electric motor.
Toyota Motor Corp's executive vice president, Takeshi Uchiyamada, told the Associated Press that new battery production lines could not be added until next year.
"Hybrids are selling so well we are doing all we can to increase production," he said. "We need new lines."
Volkswagen, Europe's biggest car maker said on Monday it wanted to produce a Golf which consumed three to four litres of petrol per 100 kilometres compared with 4.3 litres currently for the most fuel-efficient model.
"In the next few years, we are not going to do without petrol and diesel motors, but the future belongs to the electric car," VW chairman Martin Winterkorn told German newspaper Bild-Zeitung.
You can see how this Hydrogen (protron exchange) fuel cell works
Click here to get this technology full material and run your car on water rather than very expensive fuel.