Former Malmo FF manager Age Hareide is the new national coach, Denmark's football association said on Thursday.
The 62-year-old former Norway international signed a two-year contract with an option for two more years, the association, known as DBU, said.
Hareide will begin in his new job on March 1 in time for Denmark's 2018 World Cup qualifying campaign that kicks off in the second half of 2016.
"We need to try to get to the World Cup" in Russia, he told a televised news conference.
Hareide has coached several Scandinavian clubs, and was in charge of Norway from 2003-08. Last week, he announced his departure from Malmo after two years in the job.
Hareide played for Hodd and Molde in Norway before signing with Manchester City and Norwich City. He was capped 50 times for Norway.
After his playing career, he became a coach and won league titles in the three Scandinavian countries: in Sweden, with Helsingborg IF in 1999 and Malmo in 2014; in Denmark, with Brondby in 2002, and in Norway, with Rosenborg in 2003.
"I am proud, happy, and humble to be Danish coach and taking over after Morten Olsen, whom I know personally," he added.
Olsen ended his 15-year tenure last month when Denmark failed to qualify for the 2016 European Championship.
Olsen took the Danes to four major championships; the 2002 and 2010 World Cups, and Euro 2004 and 2012. He was the first Dane to reach 100 national team matches as a player and coach.