The merger, which was provisionally agreed in November last year, is expected to be completed by the end of the year.
In a statement the two companies said the deal would be a boost for shareholders, employees and customers.
The move is estimated to save the companies £350m a year in costs.
The group will operate under the banner of International Airlines Group, but the BA and Iberia brands will continue to operate as normal.
BA shareholders retaining 55 per cent ownership of the company.
In total, which will have its headquarters in London, the group will operate 408 aircraft and carry more than 58 million passengers a year, the two companies said.
The completion of the merger is subject to approval from authorities including the European Commission.
British Airways and Iberia shareholders must also give the go-ahead.
British Airways chief executive Willie Walsh said: "The merged company will provide customers with a larger combined network.
"It will also have greater potential for further growth by optimising the dual hubs of London and Madrid and providing continued investment in new products and services."