Born in Wrexham to a Greek Cypriot father and an English mother, Koumas was eligible to play for Cyprus, England and Wales. When he received call ups for both Cyprus and Wales, he opted for the latter. Koumas played 34 times for his country, making his international debut against Ukraine in 2001. He was part of Mark Hughes’s Welsh team which narrowly missed out on qualification for Euro 2004, losing 1–0 to Russia in the play-offs.

Koumas made his professional debut for Tranmere Rovers in the 1998–99 season. A series of impressive performances over the next four years won him many plaudits, including a place in the PFA Division Two team of the year for 2001–02. Koumas established himself as a talented youngster with immense potential. He scored one of Tranmere’s goals when they knocked out Merseyside rivals Everton in the 2000–01 FA Cup in a memorable 3–0 victory at Goodison Park. In August 2002, this potential was spotted by then West Bromwich Albion manager, Gary Megson, who paid Rovers a fee of £2.25 million to secure his services.

A successful first season at Premiership level, including sensational solo goals against Manchester United and Blackburn Rovers, saw Koumas win the club’s Player of the Season award. However, this was not enough to prevent Albion from suffering relegation to the Football League. Koumas inspired the Baggies promotion back to the Premiership in 2004, winning the First Division player of the month award for November 2003, as well as being named in the First Division team of the year. In the summer of 2004, Koumas signed a new contract with Albion, but during the following season fell out with new boss Bryan Robson. Robson stated that he was “disappointed” with Koumas’ attitude and placed him on the transfer list.

His international career was blighted by his persistent failure to turn up to training. In May 2006, he pulled out of a squad get-together in San Sebastián. He came back onto the international scene with three goals in two matches, one in a 3–1 win against Cyprus in October 2006 and two in a 4–0 win in November 2006 against Liechtenstein.

His club career was then rejuvenated under new manager Tony Mowbray, becoming a first team regular again, and put in several man of the match performances during 2006–07. He won the Powerade Championship player of the month award for December 2006. Koumas was named the Championship Player of the Year at the Football League Awards in March 2007, and was also honoured in April with a place in the Championship team of the year.

In July 2007, West Brom agreed a fee of £5.3 million with Wigan Athletic, stating that it was a head-turning offer. Koumas completed the move to Wigan on 10 July. Tranmere received a portion of the transfer fee having previously included a sell-on clause in their agreement with West Brom. He made his Wigan debut on 11 August 2007 in a 2–1 defeat away at Everton. The following month he marked his 300th career league appearance by scoring his first goal for his new club, converting an 80th-minute penalty to rescue a 1–1 home draw with Fulham. Due to injury and a lack of first team opportunities under three different managers during his three years at Wigan, Koumas was linked with a return to previous club West Bromwich Albion along with Newcastle United and Leicester City on a loan deal until the end of the 2009–10 season, however a loan move never materialised. Koumas was released at the end of 2010–11 season following his return from a loan period at Cardiff City.

Koumas captained his country for the first time on 1 June 2008, as Wales lost 2–0 to the Netherlands. He missed a penalty for Wales in a World Cup qualifier against Azerbaijan. Koumas retired from international football on 6 September 2009, having scored ten goals in 34 caps. His final appearance for Wales was in a 2–0 defeat to Finland on 28 March 2009.

On 5 August 2010, Koumas agreed a deal to re-join Cardiff City on a season-long loan, but was unable to complete the move until after Cardiff’s transfer embargo was lifted. The following day, the club’s transfer embargo was lifted and Koumas was able to register with the club two days prior to the start of the 2010–11 season. Koumas made his second Cardiff City debut in the 4–0 home victory over Doncaster Rovers, coming on as a late substitute for Craig Bellamy. Koumas’ second stint at the Bluebirds was severely hampered with injuries and further niggley setbacks. Cardiff needed a win to keep the pressure on second placed Norwich and to keep automatic promotion alive. With it 1–1 at the Keepmoat Stadium in the 87th minute, Cardiff boss Dave Jones sent Koumas on. Within 3 minutes of his arrival he curled a 25-yard free-kick into the top left hand corner. Koumas then finished the game by passing the ball past the Doncaster keeper to make it 3–1.

After being released by Wigan in 2011, Koumas remained as a free agent and considered his playing career. It was revealed by BBC on 8 July 2013 that Koumas asked to train with former club Tranmere Rovers as he attempted to rebuild his footballing career. After a successful trial, he signed a one-year deal on 1 August. On 23 May 2014, Koumas signed a one-year extension.