Net profit for the year to the end of March rose 66% to €867m (£614m; $948m), slightly ahead of analysts' expectations.
The airline's "Always Getting Better" customer experience programme had attracted "millions of new customers to Ryanair", chief executive Michael O'Leary said.
Falling oil prices also led to a lower fuel bill.
"Our AGB programme is transforming our customer experience, our service, and the way we listen and respond to our customers," Mr O'Leary said.
"We have won substantial traffic and share gains in all markets."
Passenger traffic was up 11% to 90.6 million customers, while total revenue rose 12% to more than €5.6bn.
To cope with rising demand, Ryanair said it had ordered 183 Boeing 737-800 planes for delivery from 2014-18, and 200 Boeing 737 Max 200s from 2019-2023.
The new aircraft will be cheaper to finance and operate, with engines 18% more efficient than their predecessors, the company said.
Much of the growth in passenger numbers is being driven by its new Business Plus and Family Extra services, it added.
Who'd have thought it. Being nicer to customers has given Ryanair a big jump in profits, a big jump in passengers and much fuller planes.
By "being nicer" I don't just mean being more friendly. As one analyst told me, it's more concrete than that. They've got a better website. An app. They're not as draconian about their luggage rules, and you can pay more to secure a seat next to your family/friends etc.
Even by their standards, the double-digit rise in passenger numbers is big. And Ryanair has ambitious expansion plans too. With hundreds of new planes on order, they want to double the number of passengers within a decade or so.
Ryanair owns 29.8% of rival Irish airline, Aer Lingus, and has tried unsuccessfully to take over the firm in the past.
But Aer Lingus is now a takeover target for International Airlines Group (IAG), which owns British Airways and Iberia.
In February, the Irish government, which owns 25% of Aer Lingus, said it could not yet approve a £1bn offer from IAG for the carrier, because it wanted more clarity on guaranteeing jobs and more information on IAG's transatlantic plans.
Aer Lingus, however, has welcomed IAG's offer.
For its part, Ryanair said: "The Board of Ryanair will consider any offer (should we receive one) from IAG on its merits, if or when it is received."
Chief financial officer Neil Sorahan told the BBC that "there's nothing on the table at the moment".
Irish airline Ryanair has reported a big increase in full-year profits.