"These events send a strong signal to the illegitimate regimes in Venezuela and Nicaragua that democracy and the will of the people will always prevail," Trump said in a statement on Monday.
Trump also praised the role of the Bolivian military, which forced Morales to step down, reports Efe news.
"The US applauds the Bolivian people for demanding freedom and the Bolivian military for abiding by its oath to protect not just a single person, but Bolivia's constitution," he added.
In his statement, Trump also said that with Morales resignation was a "significant moment for democracy in the Western Hemisphere".
The US leader went on to say that with Morales' departure, the hemisphere is one step closer to being fully democratic, prosperous and free.
Both Maduro and Ortega have denounced the situation in Bolivia as a coup and have expressed their support for Morales, just as have Mexican President Andres Manuel Lopez-Obrador, Cuba's Miguel Diaz-Canel and Argentina's President-elect Alberto Fernandez.
The whereabouts of Morales were not known after he announced his resignation on Sunday, but on Monday Mexican Foreign Secretary Marcelo Ebrard announced that the former Bolivian leader had formally requested and been granted asylum in Mexico.
The Bolivian leader's resignation comes after he announced that a new presidential election will be held and the country's electoral entity would be completely restructured amid denunciations of irregularities in the October 20 vote by the Organization of American States in which he had been re-elected to a fourth term.
Many had complained that the vote was rigged to ensure he remained in power.
OAS Secretary General Luis Almagro, meanwhile, urged the Bolivian legislature to meet on an "urgent" basis and "ensure" that the country's institutions continued to operate properly during a transition period leading to the new election.
( With inputs from IANS )