After fewer than eight months in office, Mr Tsipras has faced splits in his left-wing Syriza party over a third loan from his Greece's international creditors.
The deal included deep public sector cuts including pension reforms to secure €86bn over the next three years and remain in the eurozone.
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Following the acceptance of the deal, Mr Tsipras said he “did not achieve the agreement we expected before the January elections".
In a televised address announcing his resignation, he said Syriza’s political mandate had “exhausted its limits”.
"I feel the deep ethical and political responsibility to put to your judgment all I have done - successes and failures," he said.
Some reports have suggested the election will take place on 20 September, although an official timetable is yet to be announced.
Yesterday Greece received the first tranche of its bailout, worth €13bn, in time for a repayment of €3.2bn it owes to the European Central Bank.
Some 118 of Mr Tsipras' MPs voted in favour of the bailout, while he would need 120 to survive a confidence vote.