Irish MPs voted by a majority of 23 according to local media reports, ending two days of tense negotiations.
The vote comes after the Irish government agreed to sell its 25 per cent in Aer Lingus to IAG earlier this week, saying that IAG had made "a number of extremely important changes" to its initial offer.
The government said it did not foresee any redundancies and that another 635 jobs could be created by 2020.
IAG now needs to buy the stake owned by Ryanair, which has 29 per cent of the former flag carrier's shares, however it's previously voiced its support for earlier bids.
If the deal completes it will bring Aer Lingus back under the leadership of Willie Walsh, IAG’s chief executive. Walsh was boss at Aer Lingus from 2001 until 2005.