The Direct Energie rider took advantage of a lapse in concentration from Team Sky's Nicolas Roche to beat the Irishman in a sprint finish.
Roche was also second in the overall standings, six seconds behind Voeckler.
Bury's Adam Yates (Orica) was Britain's highest finisher, as he was third in the stage and fourth overall.
Sunday's final stage, a 198km route from Middlesbrough to Scarborough, contained six categorised climbs.
Team Sky set a punishing pace in wet and gruelling conditions after taking it on at half distance and with 44km to go they had five riders at the head of the leading group.
Roche attacked on the ascent at Harwood Dale and took with them Voeckler, Yates, Anthony Turgis (Cofidis) and Steven Kruijswijk (LottoNL).
It was Voeckler who clung on the to back of Roche as the Team Sky sprinter attacked again in the descent into Scarborough.
Voeckler, who finished third last year after missing out in a sprint finish, used that experience to employ some cat and mouse tactics, as he tracked Roche along the resort's seafront in front of huge crowds on the town's famous grass banks.
Roche suffered a momentary lapse in concentration, causing him to look the wrong way as Voeckler flew past him with the finishing line in sight to leave his rival in his wake.
Voeckler told ITV4: "It wasn't just with the strength in my legs that I used, but also my head.
"It was difficult to follow the attack of Team Sky at the climbs, so I decided on a little more patience.
"Then I knew to launch the sprint at 300 metres. Although it was early, with the wind at my back, it was not so bad."
And in a tribute to the Yorkshire public that came out in huge numbers despite persistent drizzle, he added: "I feel like this is home because the crowd were shouting my name."
The Tour de Yorkshire is a legacy of the county's hosting of 2014 Tour de France's Grand Depart. More than two million people are estimated to have lined the three-day route.
Frenchman Thomas Voeckler clinched overall victory in the Tour de Yorkshire by winning the third and final stage at Scarborough.