Born in Santiago de Compostela, Galicia, Veloso played professionally with Deportivo de La Coruña, Real Madrid, CD Ourense and Rayo Vallecano. With the second club he was used almost exclusively as a reserve, but still managed to score nine goals in only 16 games in the 1966–67 season to win the first of his three La Liga championships with the team; additionally, he netted three times in just five matches in the European Cup, being part of the squad that won the 1966 edition.