Born in Lisbon, Portugal, Veiga played for several local clubs as a youth, finishing his development at G.D. Estoril-Praia and going on to spend his first four senior seasons with them, three in the second division and one in the third.
In 2000 he signed for Vitória de Setúbal, contributing with 17 games and one goal in his first year as the Sadinos returned to the Primeira Liga.
After two more years with Vitória, Veiga returned to the second level and joined Associação Naval 1º de Maio, achieving another top flight promotion in 2005, the Figueira da Foz club's first ever.
[1] In the summer of 2006, after helping the team retain their league status, he left Portugal for the first time, going on to spend the following four seasons in Cyprus with AC Omonia and AEK Larnaca FC.
He played every match in the 2006 FIFA World Cup qualification stage, only missing the fixtures against Burkina Faso and Uganda.