Addressing a special session of parliament, Ouattara described 73-year-old Duncan as "devoted, a loyal collaborator" and "a patriot and great servant of the state".
The new post of vice-president was set up under constitutional changes voted by referendum and approved in November.
Some analysts have said the new VP could be well-placed to step into Ouattara's shoes in the future.
Duncan's nomination comes a day after he and his government resigned following legislative elections in December.
Coulibaly "will propose a new government as soon as possible," a statement said.
Former rebel leader Guillaume Soro, who served as premier for five years until 2012, was re-elected parliament speaker on Monday.
Also on Monday, Ouattara fired the heads of the country's armed forces and police after a brief army mutiny that stoked security fears in the world's top cocoa producer.
The two-day revolt was worst in the country's second city of Bouake, the cradle of a failed attempt in 2002 to oust then president Laurent Gbagbo.
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