Berlin, acting through the Financial Markets Stabilisation Fund SoFFin, said it would offer shareholders €1.39 ($1.85 dollars) per share.
"The offer price of €1.39 per HRE share represents a premium of approximately 10 percent to the statutory minimum offer price of €1.26," a SoFFin statement said.
Stressing that the operation was a "voluntary public takeover offer to the shareholders of Hypo Real Estate," it said further details would be released "within the next few days after approval by (the stock market regulator) BaFin."
SoFFin said it intended to acquire 100 percent of the outstanding HRE shares but added that it had set no minimum acceptance level.
The move was aimed at "stabilising the German financial market," as authorities feared a collapse of HRE could be as damaging as the bankruptcy of US investment bank Lehman Brothers in September.
Germany recently passed a controversial law allowing the state to nationalise HRE, by force if necessary but only as a last resort.
The legislation would enable Berlin to seize the shares of US investor Christopher Flowers, who heads a consortium that owns almost 24 percent of HRE.
The state currently owns 8.7 percent of HRE, a specialist property lender that has received more than €100 billion ($132 billion) in private and public aid so far to keep it afloat.
The bank posted a 2008 net loss of €5.46 billion as it struggled in the fallout from the worst global slump since the 1930s.