Rival bidder Goldman Sachs has until June 16 to come up with a counter offer.
Airports operator BAA has agreed a takeover by giant Spanish construction firm Ferrovial.
BAA, which operates Heathrow, Gatwick and Stansted, agreed late last night to an offer which values the firm at £10bn: a share offer of 950p per share.
Ferrovial saw off a rival bid from US bank Goldman Sachs, which offered a deal worth 955.25p per share.
The US bank has been given until 16 June to come up with a counter-offer.
Both bids would increase BAA's debt, leading to question marks over the future of big investments to be made in its airport stock. Heathrow Terminal 5 is winding down, but future schemes such as the new Terminal East or work at Stansted could come under scrutiny.