To mark the centenary, Hollande and Merkel will lay wreaths at cemeteries holding the dead of both sides in the northeast French town.
The 1916 offensive lasted 300 days and claimed more than 300,000 lives.
Both leaders are expected to use the day of remembrance to stress the need for unity at a time when the European Union is under pressure from the migrant crisis and a possible Brexit.
"To be invited to these commemorations shows the extent to which relations between France and Germany are good today," she said.
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In the run-up to the ceremony, Hollande recalled the moment during the 1984 commemoration that his predecessor Francois Mitterrand and the then chancellor of West Germany Helmut Kohl joined hands during the playing of the French national anthem.
"Mitterrand's gesture with Helmut Kohl, the hands that reached out and found each other, that's the symbol of reconciliation," he told French radio this week.
That appeared to be a reference to Europe's far-right parties which have made advances in several countries, fuelled by growing concern over an unprecedented influx of migrants.
European Commission President Jean-Claude Juncker will also attend today's acts of remembrance.
Hollande and Merkel will start by visiting the German military cemetery at Consenvoye, just north of Verdun.
At a lunch today the two leaders will then discuss the crisis caused by the hundreds of thousands of migrants and refugees seeking refuge in Europe and the June 23 British referendum on whether or not to quit the European Union.
Then they will attend a ceremony at the Douaumont ossuary, where the remains of 130,000 soldiers, French and German, lie underground.