FIRB notified the parent company that there were no objections to its acquisition of a higher stake in Leighton under the Australian government's investment policy.
Hochtief is controlled by Spanish construction giant Grupo ACS.
Its offer of $A22.50 per share for three out of eight shares is now unconditional.
Approval of the offer follows the majority shareholder's move to replace former Leighton CEO Hamish Tyrwhitt with Hochtief CEO Marcelino Fernandez Verdes.
In addition, former Leighton chief financial officer Peter Gregg was replaced by Javier Loizaga.
As a result of the takeover, Hochtief said some roles at Leighton might be made redundant and some of the company brands, such as John Holland and Thiess, could be merged or dropped.
“As a result of the general review by Leighton already underway, some employees may become redundant,” Hochtief said when it released its bidder statement in mid-March.
“A particular focus of the review is whether the existing operating businesses of Leighton can be more efficiently structured.”
The review is expected to be completed by the end of the year. Subject to its outcome, more management changes may be made.
Leighton released its bidder statement yesterday, urging shareholders to accept the bid by the time the offer closes on May 9.
Shares in Leighton were down 0.5% to $20.055.