The plan will be revealed as chief executive Michael O'Leary announces the company's half year results.
"Economy class will be very cheap -- around €10," Mr O'Leary said.
"But our business class will be very expensive. There's always 10pc to 15pc who'll pay whatever it costs for a wide seat," he said.
The €10 flights -- which could begin by the end of next year -- would be available for those booking early.
Passengers would pay airport taxes on top of the fares.
Mr O'Leary is expected to announce plans to buy more than 50 aircraft as part of his vision to help Ryanair beat the recession.
"We'll just have to keep flying more aircraft, opening up more routes and offering people more cheap flights," he said.
The transatlantic flights are likely to go from Stansted and Dublin airports to New York, Florida, Los Angeles, San Francisco and Boston.
O'Leary believes he will be able to buy 50 to 60 jumbo jets on the cheap -- then offer flights to the US that will cost less than the taxi to the airport.
His €10 tickets are a far cry from the current £578 (€729) cost of a British Airways economy flight from London to New York -- and are likely to prompt a price-cutting war between airlines.
But, as with Ryanair's European flights, passengers will have to get in early to grab the cheapest tickets -- and airport taxes will be added to the cost.
The firm will make profits on duty-free sales and by charging extra for food and in-flight entertainment.
Ryanair's long-haul flights will also include a pricey business class expected to provide beds, showers and limousines to the wealthy for around €5,000.