Ferrovial has sold the 5.9 per cent stake to US infrastructure-focused investment fund Alinda Capital Partners for €325m (£280m).
The sale values BAA at £4.8bn, more than double the consensus value analysts have placed on it.
The news has boosted Ferrovial’s share price and means it no longer has to include BAA’s debt on its balance sheet.
Ferrovial chief executive Inigo Meiras said the sale was “in line with our strategy to establish a market valuation of our assets."
BAA’s value has been hit by its failure to overturn a Competition Commission decision to force it to sell two of its London airports and one of its Scottish hubs to combat its controlling position in the UK market.
BAA has already sold Gatwick and must now sell Stansted and either Glasgow or Edinburgh.
The stake sale means Ferrovial will slash the debt it reports on its balance sheet by more than two-thirds to €5.2bn from €19.75bn.