Costa, 27, crossed 14 seconds ahead of Dutch rider Bauke Mollema with Swiss Mathias Frank 24sec off the pace in third following the 156.5 kilometre run from Martigny to Saas-Fee.
   
Germany's Tony Martin, who had been wearing the leader's yellow jersey since stage one, finished off the podium in overall fourth behind Costa, Frank and Mollema.
   
World time-trial champion Costa, who finished third in the Tour of Romandie last month, sets himself up as a candidate for the Tour de France which starts on July 5th.
   
The Portuguese could count on his experience to see him through to a third title after 2012 and 2013, as the Lampre rider, leading a nine-man breakaway group, took Martin by surprise.
   
Costa stage managed the race over the final two days in the mountains sticking close to Martin on the penultimate stage at the summit of Verbier to claim victory on the final beyond category climb at Saas-Fee.
   
The Portuguese rider went off with a breakaway group under cloudy skies at the 46-kilometre mark with his advantage on the peloton, in which Martin found himself, more than two minutes 20 kilometres from the line.
   
Attacking on the final two kilometre climb Costa left no chance to his fellow breakaway riders including home hope Frank, who had the consolation of second in the overall standings.