The deal could end years of dispute between the two countries - dating back to 2007 when Bavarian bank BayernLB bought Hypo Alpe Adria, which was nationalised by Austria two years later.
"It's a step in the direction of a settlement," Chancellor Werner Faymann said on Tuesday, adding that a deal could be done by September.
The €1.23 billion represents 45 percent of Bavaria's claims, and Vice-Chancellor Reinhold Mitterlehner said Austria would add 45 percent of any gains Heta might make in future.
The failure of Hypo Alpe Adria sparked multiple lawsuits in Austria and Germany with claims and counter-claims amounting to about €16 billion.
Hypo Alpe nearly collapsed over bad loans in the former Yugoslavia.
After €5.5 billion of state aid and growing public discontent, Austria's government halted further support for the bank in March.
Heta is the first European bank to be wound down under the EU's Bank Recovery and Resolution Directive, a new law designed to protect taxpayers from the cost of bank failures.
The main investors in Heta's bonds are German state-owned banks, mortgage banks and insurers.
Heta said in a statement it welcomed the negotiations, in which it was not involved.