Addo started his career in 1991 in Hamburg, but failed to make an impression there. He then moved to Hannover 96 in the Regionalliga Nord (third German league). He made a big impression in a squad that featured stars-to-be Gerald Asamoah and Fabian Ernst. That team ripped through the season scoring more than 100 goals, but succumbed to Energie Cottbus in the 1997 promotion playoffs.
In 1998, Hannover finally promoted to the Second Bundesliga. In his first season, he scored seven goals in 30 games and was acknowledged as one of the elite players of the league. He then transferred to Borussia Dortmund in 1999 and played more than 75 times for the team, becoming German champion in 2002. However, he was also hampered by great injury troubles, as he tore his cruciate ligaments three times in this time, the first coming after a German Cup match against SC Freiburg on 15 July 2001. The player had an MRI scan which showed he had torn knee ligaments and underwent surgery on his right knee on 22 July at the Vail, Colorado clinic of world-renowned knee specialist surgeon Dr. Richard Steadman. He healed completely after that, and came back to play the 2002 UEFA Cup Final for Dortmund against Feyenoord Rotterdam on 8 May 2002, which Dortmund lost 3–2 at the Feijenoord Stadion in Rotterdam. On 7 September 2002, Addo tore right knee ligaments for the second time, in a 2004 African Cup of Nations qualifier versus Uganda in Kampala.
On 24 September 2003, Addo's career was under threat after he re-injured his troublesome right knee for the third time in Dortmund's 2–1 UEFA Cup victory over Austria Vienna. He started the match, but was replaced after just 38 minutes.
After sitting out the whole of 2004, Addo returned to action as a substitute in Dortmund's 1–1 league home draw with Borussia Mönchengladbach in the last weekend of January 2005. At the beginning of the 2005–06 season he transferred to FSV Mainz 05, for whom he did not make an initial impact. However, he played well enough to earn a nomination for the Ghanaian squad who appeared at the 2006 World Cup.
On 9 August 2007, Addo signed a three-year contract with hometown Hamburger SV, initially alternating with the reserves and the first team. While at Hamburg, Addo revealed his Hamburger goals in an interview with HSVLIVE, also addressing other topics.
In December 2013, Addo was appointed as the head scout of the Ghana national football team and prior to the 2014 FIFA World Cup and 2015 Africa Cup of Nations, succeeding Ibrahim Tanko following the 2012 Africa Cup of Nations and 2013 Africa Cup of Nations.
Although born in Germany, Addo has been a full Ghana since 1999, his debut coming in a 5–0 rout of Eritrea on 28 February 1999, and shot to international prominence when he led the nation in the 2000 African Cup of Nations. Along with Hans Sarpei from VfL Wolfsburg, he is one of two Ghanaians with German roots who play for the African side. He started for Ghana as right midfielder in the 2006 FIFA World Cup game against the Czech Republic on 17 June 2006 at the RheinEnergieStadion in Cologne, which Ghana won 2–0. He also played in Ghana's 2–1 win over the United States at the Frankenstadion in Nuremberg.
Addo was strong in one-on-one situations, physical, creative, and versatile enough to play on both wings, on the inside and also in the central position, although his main skill was his ability to dribble the ball.Borussia Dortmund
UEFA Cup: Runner-up 2001–02