Shares in airlines have jumped after Ryanair voted to accept International Airlines Group's (IAG) offer for its 29.8% stake in Aer Lingus.
The formal acceptance paves the way for the €1.3bn (£940m) bid by BA and Iberia owner IAG for Aer Lingus to go ahead.
It is subject to backing by competition authorities. European Union approval is now the last remaining hurdle to the tie-up.
IAG's plans include building a new transatlantic hub at Dublin airport.
Ryanair's chief executive Michael O'Leary said in a statement: "We believe the IAG offer for Aer Lingus is a reasonable one in the current market and we plan to accept it, in the best interests of Ryanair shareholders.
"The price means that Ryanair will make a small profit on its investment in Aer Lingus over the past nine years."
Ryanair has attempted to buy Aer Lingus three times. Its takeover quest began in 2006, just after Aer Lingus was floated on the stock market by the Irish government.
Ryanair's initial bid illustrates the wild swings in Aer Lingus's value since then. Its first offer was €2.80 a share. The second, two years later, was half that and its most recent offer in 2012 was €1.30 a share.
The Irish government, which sold its 25% stake in Aer Lingus to IAG in May, recommended that Ryanair accept IAG's offer.
The deal values Aer Lingus shares at around €2.50 (£1.87) per share.
Aer Lingus is Heathrow Airport's fourth busiest operator, behind BA, Lufthansa and Virgin Atlantic.
If the deal is approved, IAG would gain more take-off and landing slots at Heathrow Airport, allowing it to operate more flights.
Ryanair said it had planned to use Aer Lingus to gain slots at mainstream airports.
Travellers have been surprised in the past by the distance of some of Ryanair's airports from the city they thought they were flying to.
Michael O'Leary said Ryanair did not need Aer Lingus now: "Our original strategy for Aer Lingus (to use it as a mid-priced brand to offer competition to flag carriers at primary airports) has been overtaken by the successful rollout - since Sept 2013 - of Ryanair's "Always Getting Better" strategy, which has seen the Ryanair brand successfully enter many of Europe's primary airports."