The Finn, who was been the team's test driver for the last two years, steps up in place of Brazil's Bruno Senna.
Venezuela's Maldonado has been rewarded for winning this season's Spanish grand prix, the team's first race victory since 2004, with a third year at the team.
"In Pastor and Valtteri we have two of the most exciting talents in motor racing and I am especially excited about what 2013 can bring for Williams," said Frank Williams, the team principal.
"Pastor has always demonstrated remarkable pace and this year has seen him mature as a racing driver. Valtteri is quite simply one of the most talented young racing drivers I have come across and we expect great things from him in the future."
The 23-year-old Valtteri, a protégé of McLaren's double world champion Mika Hakkinen, has been groomed by Williams over the past two years and his lap times during race weekends this season have been impressive.
He was even being linked to McLaren as a possible replacement for departing 2008 world champion Lewis Hamilton.
"It has always been my lifelong dream to compete in the Formula One World Championship," he said.
"To do so with one of the most legendary teams in the sport is incredibly special."