Kavanagh, who will remain with Aer Lingus as a non-executive director, is stepping down to pursue other interests, after a career that spanned over three decades at the Irish airline, with the last four in the top job.
IAG Chief Executive Willie Walsh credited Kavanagh with modernizing Aer Lingus, the flag carrier of Ireland founded by the government in 1936.
Doyle, who hails from Cork, Ireland, is also the director of network, fleet and alliances at IAG-owned British Airways.
IAG also said Mike Rutter, chief operating officer of Aer Lingus, has extended his contract with the airline.
(Reporting by Shariq Khan in Bengaluru; Editing by Kirsten Donovan and Emelia Sithole-Matarise)