"It is up to us to take the necessary decisions for the European Union and the eurozone, to prepare our societies for the future and protect and advance prosperity in a sustainable way," Merkel wrote in a letter which also congratulated Hollande on his poll victory.
Merkel noted that Hollande was assuming power in the European Union's number two economy, "at a time full of challenges".
"I am sure that our cooperation will continue to strengthen and deepen the traditionally close friendship between our peoples as we look ahead to the 50th anniversary of the Elysee treaty" between France and Germany next January, she said.
"I look forward to continuing with you on the path of assuming our shared responsibility for Europe and to working for the benefit of our countries and Europe," Merkel said.
Merkel said Monday that she would welcome Hollande with "open arms" when he makes his first foreign trip as president to Berlin, most likely on Wednesday 16, the day after he officially assumes his role as president.
But she also made clear she had no plans to renegotiate the fiscal pact setting tough budgetary rules for EU states that she spearheaded, despite calls by Hollande to rework it to do more to foster growth.