At Ajax, he was coached by fellow Dane Morten Olsen, and played alongside Danish international Ole Tobiasen.

[2] In October 2000, Grønkjær joined Premier League club Chelsea for £7.8 million,[3] which made him the then most expensive Danish football player.

The importance of this result cannot be overstated, as qualification for the Champions League was considered essential to Roman Abramovich's impending takeover of the club, which was at the time in some financial difficulty.

"[7] In the 2003–04 UEFA Champions League quarter-final second leg away at Highbury, Grønkjær came on for Scott Parker in the second half, with Arsenal leading 1–0 on the night and 2–1 on aggregate.

As Wayne Bridge scored three minutes before the final whistle, Chelsea went on to defeat Arsenal 3–2 on aggregate and book a place in the semi-finals.

Chelsea had fired manager Claudio Ranieri before UEFA Euro 2004, and Grønkjær signed for Birmingham City for £2.2 million in July 2004.

[13] Grønkjær struggled to settle in Spain and, following putting in a transfer request, made a reported €6 million move to Bundesliga club VfB Stuttgart in the summer of 2005,[14] where the club was building a formidable squad under manager Giovanni Trapattoni and Grønkjær would play alongside fellow Dane Jon Dahl Tomasson.

On 6 December 2006, he scored the second Champions League goal of his career, against Scottish team Celtic in a match FCK won 3–1 at the Parken Stadium.

Grønkjær played the highest number of games in his Copenhagen career during the 2009–10 football season, as he helped the club win the 2009–10 Danish Superliga championship.

"[24] He played his last game against his first professional club AaB,[25] and scored the final goal in a 2–0 victory for Copenhagen.

In his first year at Ajax, Grønkjær made his full international debut for the Denmark national team in the 2000 European Championship (Euro 2000) qualification game against Italy on 27 March 1999.

In the very first minute of the game, he famously echoed Jesper Olsen's 1986 World Cup mistimed back pass to Spanish forward Emilio Butragueño, as Grønkjær passed the ball to Italian forward Filippo Inzaghi who promptly scored the first goal in Italy's 2–1 victory.

In the qualification games for Euro 2004, he scored the game-winning goal in a 1–0 victory over closest rivals Norway, helping Denmark qualify for the final tournament in Portugal.

He missed the opening game of Euro 2004 due to the death of his mother, but went to Portugal to join the Danish squad and scored the second goal of the 2–0 win against Bulgaria.