The Portuguese rider returns from a shortened doping suspension after having tested positive for Methylhexanamine at the national championships last year, where he took the time trial title.
The positive test result was made public in October 2010, but Costa and his brother, who was also positive, were able to show that they ingested the banned substance through a contaminated food supplement.
Costa has already raced for Eusebio Unzue in the past, as he was a member of Caisse d'Epargne in 2009 and 2010. The 24-year-old won the eighth stage of the Tour de Suisse last year, and the 2009 Four Days of Dunkirk. Movistar has signed Costa on a three-years contract.