The 300 days of fighting in northeast France were one of the bloodiest battles of the war, claiming more than 300,000 lives before France emerged victorious.
Hollande and Merkel said just as France and Germany had put aside their shared history to become close allies, the European Union must now pull together to deal with the migrant crisis and a possible British exit in a referendum next month.
"Our solemn duty is written in the ravaged ground of Verdun... Let's love our own people but let's protect our common home, Europe, without which we would be exposed to the storms of history," Hollande said.
Merkel, whose country took in more than one million refugees in 2015, said the challenges of the 21st century "can only be overcome together".
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The lessons for Europe from the "catastrophes" of the 20th century were that "it is essential not to shut ourselves off, but to be open to each other," Merkel said.
Under persistent rain, the two leaders began the day of commemoration by laying a wreath at the German military cemetery at Consenvoye, just north of Verdun.
Sharing an umbrella, they walked between rows of black crosses inscribed with the names of the German dead stretching down the hill where 11,000 soldiers are buried.