Spanish builder ACS has bought a 5.8 percent stake in Hochtief to raise its holding in the German group to 66.54 percent.
The shares were part of a placement by the Qatar Investment Authority (QIA), which divested its Hochtief stake of around 10 percent as part of a portfolio reshuffle.
QIA placed 7 million shares in Hochtief for 77 euros apiece, fetching around 540 million euros ($614 million), it said in a statement.
Morgan Stanley had offered the shares in an accelerated bookbuilding with a guidance of 76.50 euros to the market close of 81.78 euros.
The QIA has been reviewing its investment strategy as a result of lower oil prices and following the appointment of a new chief executive in December.
It sold a 1.1 percent stake in French construction group Vinci last week.
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