The 37-year-old crossed the finish line off western France in his Smurfit Kappa-Kingspan on the third and final stage in seventh place, after more than three days and fifteen hours racing.
Frenchman Lois Berrehar at the helm of Macif 2022 won the final stage, having also won the first in Gijon in Spain.
But a delay at the finish of the second stage in Royan, France cost the 30-year-old Berrehar, and he finished second overall.
"I haven't really got my head around what's just happened yet," said Dolan, winner of the second stage.
"Today really is a dream come true."
France's Gaston Morvan finished third on the day and third overall.
On Sunday, 37 competitors sailed out of Royan heading along the French Atlantic coast and the Bay of Biscay towards Spain and up towards England where they battled windy conditions.
"It was full-on. I'd go as far as to say that it was even a little scary," said Dolan.
He becomes the third non-French competitor to win in 55 editions after Belgian Joan de Kat in 1970 and Swiss Laurent Bourgnon in 1988.
The race is regarded as one of the main springboards for offshore races such as the Vendee Globe and the Route du Rhum.
