Lawmakers of Morales’ Movement for Socialism party were not present when Añez made the announcement.
Thousands marched through Caracas on Tuesday, many carrying handmade signs scrawled with “Evo!”
Morales stepped down on Sunday at the “suggestion” of his country’s military chief following several tumultuous weeks of protests since his disputed election to a fourth term.
He was the last survivor of a so-called “pink tide” of leftist leaders across Latin America that included former Venezuelan President Hugo Chavez.
Venezuela’s socialist leaders called on sympathizers to take the streets in a march that played out as Morales landed in Mexico where he is being granted asylum.
Venezuela’s President Nicolás Maduro is a long political ally of Morales, who accused the United States of mounting an economic war to overthrow his socialist government.