[4][5] Born in Accra, Ofori-Quaye came to Greece at the age of 15, signing for Kalamata FC during the Stavros Papadopoulos era of the club.
Ofori-Quaye attracted much attention from other clubs, scoring key goals including those in the UEFA Champions League against the likes of Rosenborg BK, Olympique Lyonnais, and Deportivo La Coruna.
He won 6 Greek Championships with the Piraeus based club, a Hellenic Cup, and helped them reach the quarter-finals of the 1998–99 UEFA Champions League.
In 2005, he returned to Greece signing for OFI Crete where he began to hit good form and was recalled back to his national team.
[7] In July 2007 newly promoted Israeli club Kiryat Shmona tried to sign him, but his contract was not approved in the first place with OFI reported him missing for the past three months.
[10][11] After being out for a while due to injuries and almost signing for Accra Hearts of Oak in 2010, Ofori-Quaye returned to Ghana and joined newly promoted Ahafo based club Bechem United in 2011 on a one-year deal.
[13][14] On 6 November 2011, in a match against Aduana Stars, he missed a penalty after he had been fouled in the 35th minute, failing to double their early lead through Richard Addai.
[6] In October 2006, after being out of the national team for three years, he received a call up for Ghana's International friendly match against Australia on 14 November in London.