Costa turned professional in 2007 with Portugal's Benfica team and remained with the squad through the 2008 season where he finished fifth in the U23 world road race championship and eighth in the U23 world time trial championship in Varese, Italy.
Costa made his ProTour debut with Spain's Caisse d'Epargne team in 2009. With Caisse d'Epargne Costa won the 4 Jours de Dunkerque, the GP Credito Agricola and a stage of the Vuelta a Chihuahua. Costa also won the Vuelta a Chihuahua's mountains classification.