Hochtief is already a majority shareholder in Leighton, which is based in Sydney. The offer price is AU$18.65 (£10.11) per share.
If all Leighton shareholders accept the offer, Hochtief will increase its stake in Leighton from 58.77% to a maximum of 74.23% for a total cash consideration of approximately €755m (£627m) at the current exchange rate.
The offer will be subject to regulatory approvals and other customary conditions.
The transaction will be funded from cash reserves and undrawn facilities available to Hochtief Aktiengesellschaft.
Hochtief also announced that it intends to increase its representation on the Leighton board of directors to reflect its shareholding.
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