Vicuna, who has been in the post on an acting basis, won the support of 70 of the 137-member legislature. She was to be sworn in Saturday.
Glas, 48, automatically lost his title on Wednesday because he was absent from his post for more than the three months permitted under Ecuador's constitution -- because of his incarceration and pre-trial detention.
He is the highest-ranking Latin American politician to be convicted and imprisoned in a regional scandal involving a Brazilian construction group, Odebrecht, which gave bribes to secure public works contracts.
He was given a six-year sentence on December 13 by Ecuador's Supreme Court after being found guilty of receiving $13.5 million in Odebrecht kickbacks. He says he is innocent and will appeal.
But, taking into account his detention since October 2 pending his trial, he has not been able to carry out his duties for over three months.
Odebrecht, which was investigated by the US Justice Department, agreed to pay a $3.5 billion fine after admitting to giving $788 million in bribes across 12 countries to secure contracts.
The scandal has ensnared politicians in several countries, including Mexico, Peru, Panama and Venezuela.
Ecuadoran prosecutors said Odebrecht spent $47.3 million in bribes in their country to get public contracts.