In August, the families said they were unhappy with the latest German compensation offers and that they planned to boycott a ceremony marking the 50th anniversary of the attack in protest.
The Frankfurter Allgemeine newspaper, quoting Germany's news agency DPA, said on Wednesday that compensation of €28 million ($28m) had been discussed, of which the federal government would cover €22.5m.
Berlin did not confirm the amounts, saying the talks with the victims' representatives were confidential.
"With this agreement, the German state acknowledges its responsibility and recognises the terrible suffering of the murdered and their families," a statement by the two presidents said.
On September 5, 1972, members of the Israeli Olympic team were taken hostage at the poorly secured athletes' village by Palestinian gunmen from the radical Black September group.
Within 24 hours, 11 Israelis, five Palestinians and a German policeman were dead after a stand-off and subsequent rescue effort erupted into gunfire.
The German Interior Ministry this month said the federal government, the state of Bavaria and the city of Munich had decided to offer the families more than payments that were reportedly made soon after the massacre.
The Times of Israel reported that immediately after the massacre, Germany made payments to the relatives of the victims amounting to about 4.19 million German marks and that in 2002, the surviving relatives received another €3m.
Since the end of the Holocaust and the Second World War, during which about six million European Jews were murdered, Berlin has felt a special responsibility to make amends with Israel.
The German government also said it had agreed on an overall concept for the historical documentation of the 1972 attack by a commission of German and Israeli historians.
"In doing so, Germany is fulfilling its historical obligation towards the victims and their families," government spokesman Steffen Hebestreit said.