Goumas was born on May 24, 1975 in the village of Ampelonas, near Larisa. He is one of the many players to emerge from Panathinaikos FC's youth academy and has been in their first team since 1994. He is known for his tough tackling, excellent aerial ability and his habit of scoring goals off set pieces.
Goumas debuted with the National Football Team of Greece on February 3, 1999 against Finland and has, so far (January 2009), 45 caps to his name . He was part of the Greek squad that won the Euro 2004 Championship but did not participate in any games.