He started his career with PAOK. He also had spells with Niki Volos, Panserraikos, Diagoras, Olympiakos Volos, Pierikos, Doxa Drama and Iraklis. Konteon was brought up from PAOK"s academies and started his professional career for PAOK in 2002. While in PAOK he was loaned out to Niki Volos, where he spent the 2004-2005 season.
On 24 January 2006 Konteon signed for Panserraikos for 1.5 years, finally stayign for a mere six months.
After leaving Panserraikos he joined Diagoras for the 2006-2007 season. In 2007 he signed for Olympaikos Volos from which he was released during the 2009 winte transfer window.
He signed for Pierikos during the 2010 winter transfer window, where he spent 2.5 years making a total of 66 appearances for the club and scoring 9 times. In the summer of 2012 he reached an agreement with Doxa Drama with which he spent the 2012-2013 season.
He was released from Doxa in the summer of 2013.
On 15 July 2013 he signed an annual contract with Greek Football League outfit Iraklis. He made his debut for his new club in an away 1–0 loss against Vataniakos. He finished the season appearing in 25 matches and scoring 1 goal.
On 11 July 2014 he signed for Chania.