Tsipras submitted his resignation to President Prokopis Pavlopoulos and asked for the earliest possible election date.
Government officials said the aim was to hold the election on Sept. 20, with Tsipras seeking to crush a rebellion in his leftist Syriza party and seal public support for the bailout program, Greece's third since 2010, that he negotiated.
"I will go to the president of the republic shortly to submit my resignation, as well as the resignation of my government," Tsipras said in a televised address before he met Pavlopoulos.
Faced with a near collapse of the Greek financial system which threatened the country's future in the euro, Tsipras was forced to accept the creditors' demands for yet more austerity and economic reform - the very policies he had promised to scrap when he was elected in January.
"I want to be honest with you. We did not achieve the agreement we expected before the January elections," he told the Greek people.
"I feel the deep ethical and political responsibility to put to your judgment all I have done, successes and failures."
His decision deepens political uncertainty on the day Greece began receiving funds under its 86 billion-euro ($96 billion) bailout program, five years after a previous government took the first bailout from the euro zone and IMF.
But a snap election should allow Tsipras to capitalize on his popularity with voters before the toughest parts of the latest program - including further pension cuts, more value-added tax increases and a "solidarity" tax on incomes - begin to bite. This may allow him to return to power in a stronger position without anti-bailout rebels in Syriza to slow him down.