The airliner's decision to drive down fares in the face of weakening demand caused by the atrocities in Brussels and Paris sparked a 20% rise in traffic to 24.9 million in the third quarter.
Profits after tax more than doubled in the three months to 31 December, up from 49 million euro (£37m) in 2014 to 103 million euro (£78m) last year.
Revenues also rose 17% to 1.3 billion euro (£1bn).
The Dublin-based airline said average fares were down 1% to 40 euro (£30) in the three months to 31 December. It also pencilled in a price fall of 6% for the fourth quarter.
It said it would deliver cheaper air fares by capitalising on record-low oil prices and passing down the savings made on its fuels hedges to consumers.
The four new bases it opened in Berlin, Corfu, Gothenburg and Milan Malpensa during in the third quarter were all enjoying "strong advanced bookings", the carrier said.
The trading update came as the company also announced an 800 million euro (£609m) share buy-back programme.
Chief executive Michael O'Leary said a strong first half to the third quarter had been knocked back by "weaker pricing and bookings immediately after the terrorist events in Paris and Brussels."
He added: "We reacted to this softness by running price promotions and discounted fares to stimulate double digit traffic growth."
The company upgraded its expectations for traffic in the fourth quarter by 4% to 26%, with net profits predicted to be at the "upper end" of a range between 1.1 billion euro (£893m) and 1.2 billion euro (£931m).
Rival budget carrier easyJet saw its sales hit at the end of last year as some passengers stayed away following the terrorist attacks in Egypt and Paris, which left revenues per seat 3.7% lower over its first quarter to 31 December.
Analyst Gerald Khoo at Liberum said Ryanair's revenues were "slightly better than expected," but the costs "were slightly worse."
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