Olsen signs new deal to continue
Last November, Olsen stated he would not renew his contract which expired at the end of next year's UEFA EURO 2012 in Poland and Ukraine.
However, the former Denmark international has now reassessed his decision and admitted he had been swayed by calls of support from senior players.
"My decision to stop after the European Championships next summer was the right thing at the moment," Olsen told the Danish Football Association website. "We had embarked on a new chapter for the national team after the World Cup finals.
"No-one is above the team and therefore I made a decision I felt was right for the national team at that time. But I want to stress that under no circumstances was it due to a lack of motivation.
"During the summer I got calls from both established and newer players in the team, who asked me to reconsider. It was a necessary support from the players to both me as coach and to our common project. It gave me a good feeling that together we were doing something really good in the national team."
Danish Football Association general secretary Jim Hansen was pleased Olsen, who has been in the post for 11 years, had reconsidered.
"I have never concealed the fact that Morten Olsen is the most qualified coach," Hansen said. "It is therefore extremely satisfactory that Morten has come back to us with a clear desire to continue his work."