The group will pay €400 million for the remaining 80% of the company following the conversion of a €100 million loan into a 20% equity stake in the carrier last summer.
The move comes, IAG said, to boost the organisation’s growth opportunities in the Latin America and Caribbean market.
Luis Gallego, IAG chief executive, said the agreement will enable IAG’s Madrid hub to compete on an "equal footing" with other European hubs and consolidate its position in the south Atlantic.
"Madrid is the main gateway between Latin America and Europe and there are opportunities to expand its network, providing significant benefits to our customers, employees and shareholders," he added.
The transaction is subject to regulatory and other approvals which could take around 18 months to complete.
