Renowned for his intelligence and versatility as a player, Olsen was the captain and backbone of the Danish team that first came to international prominence and contested two European Championships in 1984 and 1988, as well as the World Cup in Mexico in 1986.
Remarkably, for a player who played mostly as a sweeper and defensive midfielder, Olsen received only a single yellow card during his international career as he became the first Dane to win 100 caps.
As a player, he spent 14 years in Belgium before finishing his career in Germany with FC Cologne, where he would later return for a stint as coach and save the club from relegation.
Before that, he won two Danish titles with Copenhagen club Brondby, and on his departure from Cologne he took up the reins at Ajax Amsterdam.
Olsen was instrumental in attracting his compatriot Michael Laudrup to the club, and together they won a league and cup double in 1998 before Olsen was forced out.
In July 2000, Olsen took over from Sweden's Bo Johansson as head coach of the Danish national team, beginning a tenure that would make him one of the longest-serving coaches in the game and the longest serving among the coaches in this tournament.
Olsen's side qualified for the 2002 World Cup and the 2004 European Championships; in both tournaments Denmark progressed from their group, only to be knocked out in the next round.
Despite missing out on the World Cup in 2006, Olsen signed a new contract that would keep him in the job until 2010, and he was given responsibility developing Danish football at all levels.
Failure to qualify for the Euro 2008 followed, but in 2010 Olsen led his team to the World Cup as they topped their qualifying group ahead of Portugal and Sweden.
With a raft of injuries to key players, the Danes failed to survive their group.
Despite the retirements of record goalscorer Jon Dahl Tomasson and influential winger Jesper Gronkjaer, Olsen's side once again topped their qualifying group for Euro 2012, beating Portugal into second place.
Olsen's reward was another contract extension until the World Cup in 2014.
His teams play a classic Dutch-influenced 4-3-3 system, with wingers often cutting inside to create opportunities for the central striker. Thanks to his extended responsibilities within the Danish FA, it is a system that is played by all age groups in Denmark.
Having already overcome Portugal twice in the last two qualifying campaigns, Olsen's belief in his system is steadfast, and he will not be changing it when they meet Germany, Netherlands and Portugal again in Group B.
Denmark may be in a period of transition, but the clarity of Olsen's vision combined with the technical ability of players like Christian Eriksen and Stuttgart's William Kvist means that they have as good a chance as any of escaping what looks like the toughest group in the tournament.