German soldiers killed some 65,000 Herero and 10,000 Nama people in a 1904-1908 campaign after a revolt against land seizures by colonists in what historians and the United Nations have long called the first genocide of the 20th century.
While Germany has previously acknowledged "moral responsibility" for the killings, it had avoided making an official apology for the massacres to avoid compensation claims.
In a statement announcing an agreement with Namibia following more than five years of negotiations, Foreign Minister Heiko Maas said the events of the German colonial period should be named "without sparing or glossing over them".
The German funding will directly benefit the genocide-affected communities, he said.
Namibia's President Hage Geingob welcomed the "historic" move, but Herero paramount chief Vekuii Rukoro dismissed a deal agreed by the two governments as "an insult" because it did not include payment of reparations.