One of the longest-serving coaches in international football, the 65-year-old Olsen took charge after Euro 2000 and led the Danes to the finals of two World Cups and two European Championships.
"After 19 years as a player in the red and white, and almost 16 years as coach, this is an emotional decision to take," he told reporters.
"I have never seen this job as work - more of a lifestyle. I have always been proud of it."
Danish media had gathered to hear him present his squad for an upcoming friendly against the United States against the backdrop of a dispute between the Danish FA (DBU) and his international players over a collective bargaining agreement.
Instead, Olsen announced his decision to stand down after next year's finals in France and said he was relieved to be able to concentrate on preparing his team.
"I will not have the distraction of people debating whether I'm here or not (after Euro 2016). The DBU will have more time to find a replacement," he said.
Capped 102 times as a player, Olsen is one of the most well-liked and well-respected figures in Danish football, but his standing has not protected him from criticism when his teams have come up short.
His most recent contract extension, granted in December 2013 after Denmark had failed to qualify for the 2014 World Cup finals in Brazil, was not greeted with wide acclaim.
Denmark top Group I on seven points after four games having played one game more in their Euro 2016 qualifying campaign than Portugal, who are in second place on six points.
Denmark's next qualifier is at home to Serbia on June 13.
(Reporting by Philip O'Connor; editing by Justin Palmer)
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