After the lower house of parliament approved the fund on Thursday, the upper house Bundesrat passed it on Friday.
The massive fund is part of a €1.8 trillion budget up to 2027 agreed by the EU's 27 members in December.
"The vote is a clear signal for European solidarity and strength," said Finance Minister Olaf Scholz, stressing that it was in Germany's interest that the entire bloc emerged strong from the crisis.
"A powerful recovery in Europe is an important prerequisite for Germany's own economic success and prosperity," he said.
Chancellor Angela Merkel sketched out the fund along with French President Emmanuel Macron in May.
The move to offer outright grants to the EU countries hardest hit by the pandemic, such as Italy, smashed through long-held stereotypes of Germany as a "frugal" country staunchly opposed to taking on others' debt.
But faced with a pandemic which spared no one, Europe's biggest economy crossed several red lines to pull itself out of a crippling recession.
It also suspended a constitutional rule that blocks the government from incurring new debt for 2020 and 2021.
Berlin, which intends to borrow a record €240.2 billion in 2021, is now seeking a halt to the no-new-borrowings rule for a third consecutive year in 2022.
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