Köhler "passed away early in the morning in Berlin after a short, serious illness and surrounded by his family", says the presidential office in a statement.
Köhler was Federal President 2004-2010 when he unexpectedly resigned after criticism of his statements about Germany's mission in Afghanistan.
In 1981, economist Köhler joined the Christian Democratic CDU, he became State Secretary a few years later and was involved in negotiating Germany's reunification.
In the early 1990s, he was a special economic advisor to Chancellor Helmut Kohl, where he participated in the creation of the EU's eurozone.
Köhler has also been a UN envoy and head of the International Monetary Fund, IMF.