The proceeds are approximately €1.1bn (£926m) and the transaction will have a retroactive economic effect, backdated to 1 January.
Hochtief Airport holds interests in the airports of Athens, Budapest, Düsseldorf, Hamburg, Sydney and Tirana. Combined, these airports handle approximately 95 million passengers annually.
Closing is expected in the second half of 2013.
"The transaction is the result of a very competitive tendering process,” said Hochtief CEO Marcelino Fernández Verdes. “We will use the released funds as planned to reduce debt and to invest in the operating infrastructure business. The transaction will further strengthen Hochtief’s financial and competitive position."