South America's longest-serving leader made the announcement after a preliminary report by the Organization of American States found a "heap of observed irregularities" in the October 20 presidential contest and said a new vote should be held.
Both Morales and Supreme Electoral Tribunal president María Eugenia Choque announced their resignations after a report cited a "heap of observed irregularities" in the disputed presidential election October 20, according to The Associated Press.
The spectacle of police abandoning their positions outside the presidential palace was an ominous development for Morales. Two officials next in line to take over the government also left as the country is in turmoil after weeks of protests.
Bolivian opposition urged Morales to resign altogether despite his promise of the new elections.
The OAS added that it was statistically unlikely that Morales had secured the 10-percentage-point margin of victory needed to win outright.
On Sunday, the Organization of American States, which monitored the elections, said it had found evidence of wide-scale data manipulation, and could not certify the result of the previous polls.
Police retreated to their barracks in at least three cities.
The Foreign Ministry said in a statement on Saturday that police officers had "abandoned their constitutional role in ensuring the safety of society and state institutions".
Cuba strongly condemned what it called a "coup" in Bolivia after the long-time president resigned.
Morales, in power for almost 14 years, said in televised comments that he would submit his resignation letter to help restore stability, though he aimed barbs at what he called a "civic coup".
Units in the southeastern city of Sucre and the opposition stronghold of Santa Cruz said they were joining a rebellion launched earlier by police officers in the central city of Cochabamba.
On Sunday, the police commander, Gen. Yuri Calderón, instructed protesting officers to get back on the street and prevent attacks by thugs loyal to the president. But a 24-hour lapse in releasing vote results raised suspicions among opposition supporters.
"The Right states Eva must resign.' I would like to inform you, brothers and sisters, to each one of Bolivia and the entire world, I won't resign", Morales, a socialist, stated in a public occasion.