During his playing career, Stelios was a winger or attacking midfielder and a well-known figure in Greek football, especially during his tenure at Bolton Wanderers and at UEFA Euro 2004, where Greece won.

Next year, in his opening season as a professional, the young striker found himself scoring six goals and impressing the scouters of clubs that participated in higher divisions.

To this day Giannakopoulos regularly attends special events at his former club and is considered a legend by the fans, notably for the determination he put into every match including the derbies against arch-rivals Panathinaikos and AEK Athens where he scored many of his finest goals.

[7] His fine form continued into the 2005–06 season which was Stelios' most successful as he was top scorer for Bolton with 12 goals, an impressive tally for a midfielder.

One of the highlights of that season was the winning goal he scored against Arsenal in an FA Cup fourth round match played at the Reebok Stadium on 28 January 2006.

On 17 March 2006, he was chosen to play in a 50th anniversary game for the pact of Rome and for the participation of Manchester United in UEFA competitions, in a match that took place in Old Trafford.

Giannakopoulos played in the second half alongside players such as Steven Gerrard, Robbie Fowler, Andrea Pirlo, Zlatan Ibrahimovic, Henrik Larsson, Gennaro Gattuso and others against Manchester United in a 4–3 loss.

At the end of the season Stelios was not offered a new contract and was released by the club[9] fuelling speculation that he would be returning to his native Greece and finishing off his career at Olympiacos.

[11] Stelios is another player who arrived at Hull City with an impressive track record, having spent 5 years in the Premier League with Bolton and winning Euro 2004 with Greece.

On 22 January 2009, six years after his first move to the UK, Stelios returned to Greece by signing for Greek side AEL on a one-and-a-half-year deal.

[14] The following season however was not as successful as Stelios struggled with injuries and even courted controversy with some comments he made to the Greek press that were seen as being disloyal to his team.

Following this success, Giannakopoulos would remain a key part of the national team, becoming Greece's top scorer in their failed 2006 FIFA World Cup qualifying campaign.