[8] Born in Aguçadoura, Póvoa de Varzim, Costa started his career at Guilhabreu, a civil parish of Vila do Conde, then went to Santa Maria da Feira.

[9] At the Portuguese national championships in June 2010 Costa and his brother Mário tested positive for the banned substance methylhexanamine,[10] which they claimed to have ingested inadvertently due to a tainted food supplement.

He escaped on the last climb of the day with 5 kilometres (3.1 mi) to go, but Team Sky's Edvald Boasson Hagen passed him in the final kilometer, and Costa protected his second place as the surging peloton crossed the finish line on his heels.

He took the third step of the podium in the Grand Prix Cycliste de Québec, winning the sprint of a group of 16 riders in hot pursuit of the two escapees, Simon Gerrans and Greg Van Avermaet, who finished four seconds ahead of Costa.

[23] Two days later, he aimed at defending his title in the Grand Prix Cycliste de Montréal, but finished eighth, once again with a 4-second deficit over the winner, Lars Petter Nordhaug.

On stage 16, Costa ended up on a breakaway where he attacked on the last climb of the day, the Col de Manse before the final downhill to a solo finish in Gap.

A few days later, Costa won stage 19 after escaping from the lead group on the Col de la Croix Fry, he ended up with another solo finish in Le Grand-Bornand.

Costa won the elite men's race at the UCI Road World Championships in Tuscany, Italy, becoming the first Portuguese rider to wear the rainbow jersey.

With this victory Costa took the yellow jersey from Tony Martin and successfully defended his title, thus becoming the first cyclist to win Tour de Suisse three consecutive times.

Costa entered the Tour de France with high hopes, aiming for a podium finish, but started to lose touch with the front riders due to bronchitis.

[32] He returned to UCI World Tour competition at the GP Ouest-France, crossing the finish line in 92nd place, 11 seconds behind winner Sylvain Chavanel.

At the Tour de France he retired due to injuries picked up in a crash, leading him to announce he would ride for stage wins in the future.