Embleton will take up her new role on 6 April and replaces Donal Moriarty who has been interim chief executive since October 2020.
She has served as chief executive and chair of IAG Cargo since 2017 and has previously held a number of senior roles at British Airways, having joined the airline in 1992, including managing director at Gatwick, director of strategy and chair of BA CityFlyer.
Moriarty will resume his role as Aer Lingus’s chief corporate affairs officer.
IAG chief executive Luis Gallego, said: “I would like to thank Donal Moriarty for his work as interim chief executive. He has done an excellent job during the most challenging year in Aer Lingus’s history.
“Lynne has huge experience within the group. At IAG Cargo she has led the company as it adapted rapidly to the Covid-19 pandemic and has made significant progress in digitally transforming the business.
“I’m confident that she has the skills to lead Aer Lingus through the pandemic and enable it to emerge in a strong competitive position in the future.”