"I want to make it clear that there is no coup d'etat in Bolivia, there is a repositioning of constitutional legality," she said, vowing to organise new elections as soon as possible.
"It is fundamental that everybody realizes that today begins a peaceful and democratic route to restore legality, and that I have given the armed forces and the National Police responsibility for guaranteeing the pacification of the country.
"I speak of a change of regime, of reversing the conditions that turned us into a totalitarian country, to build fully democratic values, institutions and procedures," she said.
"I assure you that persecutions and intimidation have ended," she added.
Morales, Bolivia's first indigenous president, announced on Sunday that he was stepping down after the military brass publicly called on him to resign amid a crisis stemming from accusations by the opposition that his October 20 election victory was tainted by fraud.
Violence associated with protests that followed the elections has so far left eight people dead, 508 injured and 460 under arrest, according to official figures, while bringing economic activity to a halt.
Supporters of Morales held marches on Wednesday in La Paz and blocked roads at various locations across Bolivia.
Anez, an opposition senator, became President following the resignations of four other officials who came ahead of her in the constitutional line of succession.
The new armed forces chief appointed by Anez, Gen. Carlos Orellana, was sworn-in Wednesday, along with the new commanders of the army, air force and navy.
A few hours later, the interim president appointed an emergency cabinet with only 11 ministers out of 20 possible.
From Mexico, where he arrived on Tuesday to take up an offer of asylum, Morales on Wednesday urged a national dialog in Bolivia and said he was ready to go back to his country "if the people ask it".
"Friendly countries, international organisms can accompany" such a dialog, he said, asking the UN to "not accept this kind of coup d'etat".
In Washington, President Donald Trump recognized Anez as the new head of Bolivia.
"We applaud the interim president of Bolivia, Jeanine Anez, for assuming this crucial role at a time of great responsibility," a spokesman for the State Department for Latin America told Efe news.