Born in Izegem, Eeckhout started his career in 1993 riding for the small Collstrop-team. He immediately started winning minor Belgian races like the Championship of Flanders and the Omloop Mandel-Leie-Schelde. In 1997 and 1998 he rode for Lotto–Mobistar–Isoglass, and then rode two years for Palmans. Eeckhout had a breakthrough season when he transferred to Lotto-Adecco in 2001, winning 11 races, including Dwars door Vlaanderen and the GP van Steenbergen.
Eeckhout struggled through the next two seasons and at the end of 2004 his contract with Lotto-Adecco ended and he needed to find a new team. He signed with the Belgian squad Chocolade Jacques and found his second youth. He started the 2005 season by winning Dwars door Vlaanderen, and went on to win major races including the Grand Prix d'Isbergues and a stage of the Three Days of De Panne.
In 2006 he continued his winning form, taking the Three Days of West-Flanders. In June 2006 he won the biggest race in his career, the Belgian National Road Championship in Antwerp by beating Tom Boonen and Philippe Gilbert. Eeckhout had another great season in 2006, winning 12 races, including the 2005-2006 UCI Europe Tour.
In the peloton he earned the nickname "Rambo" for being particularly tough during hard races in severe conditions.
