ACS, led by Real Madrid football club chairman Florentino Perez, said it had acquired 30.34 percent of the German group, which had battled furiously against the Spanish bid.
Under German law, ACS is now allowed to buy its prey's shares on the open market, opening the way for it to take a majority stake and become the largest publics work group in Europe, or third biggest worldwide.
ACS's global prospects and debt-laden balance sheet - it had €9.08 billion
in net debt on September 30 last year - would be strengthened by the acquisition of Hochtief, which has operations worldwide and no debt.
Hochtief chairman Herbert Lütkestratkötter has fought the Spanish takeover since it was launched unexpectedly December 1.
The offer closed December 29, but under German law the ACS offer is now re-opened from January 5-18 for Hochtief shareholders who had previously turned it down.
By mid-morning, ACS shares were 0.30 percent lower at €35.095 while Hochtief was down 1.17 percent at €63.51.
The ACS announcement caps a bitter struggle with Hochtief, which has described the Spanish offer as too low.
In an attempt to fend off the Spanish, it agreed December 6 for Qatar Holding to buy a 9.1 percent stake in Hochtief for about €400 million, diluting ACS's stake. Hochtief's board then formally rejected the offer December 15.
ACS, in reply, sweetened its offer to propose swapping nine of its shares, instead of eight, for every five shares of Hochtief.
And the German firm's defence then took a body blow when major US-based shareholder Southeastern Asset Management announced December 16 it had lost
confidence in the Hochtief management and was selling roughly half of its 4.84-percent stake in the company to ACS.
A Southeastern statement said it had lost confidence in the management team because of "recent unacceptable steps," a reference to Hochtief's defensive sale of a 9.1 percent stake to Qatar.
ACS owned around 27.2 percent of Hochtief when it announced the offer and with the Southeastern Asset Management stake it already had close to 30 percent of the German firm.
Hochtief appeared to have accepted the inevitable success of the ACS offer when it reportedly made an agreement last week with its creditors smoothing the way for the Spanish entrant.