Gunning, who joined British Airways in 1998 and has been its CFO since January 2016, will take over from de Lôme at IAG's annual general meeting in June, the company said.
"After eight years as CFO of IAG and prior to that, 20 years as CFO of Iberia, I believe now is the right time for me to leave IAG," de Lôme said.
IAG did not immediately respond to a request for comment on the reason for de Lome's departure.
Gunning takes the role as the airline industry braces for a potential hit from Britain's impending exit from the European Union.
Shares of IAG jumped to session highs after the announcement and were last up 1.1 percent at 548.4 pence on London's main index.
(Reporting by Shashwat Awasthi and Noor Zainab Hussain in Bengaluru; Editing by Bernard Orr)