"With your vote, you will decide who ... will lead Greece into this difficult but hopeful (path forward)," he said in a televised address. "I will ask for the vote of the Greek people in order to govern and unfold our program."
The announcement by Tsipras, who came to power only last January, comes a month after Parliament agreed to severe economic measures -- such as raising certain sales taxes and overhauling the pension system -- so that Greece could receive a fresh bailout worth as much as 86 billion euros ($95 billion).
After Tsipras' address, he met late Thursday with President Prokopis Pavlopoulos, to whom he handed his resignation. The date of the election wasn't immediately announced.
Tsipras made the move after a key vote on August 14 in which Parliament approved the third bailout deal. Although the deal passed, it relied on the support of opposition lawmakers, as a significant number of members of his own party voted against it. The rebellion from his party effectively showed that he no longer had enough support to sustain a governing coalition.
He could have called for a vote of confidence but opted instead to resign and go straight for early elections.
The bailout, which helps prevent Greece's exit from the euro currency, is the country's third in roughly five years. Greece received the first installment of the latest bailout -- 26 billion euros ($29.1 billion) -- on Thursday. Athens in turn made a 3.2 billion euro ($3.6 billion) loan repayment to the European Central Bank.
Tsipras' own left-wing Syriza party rallied against the reforms, but Tsipras and the Parliament accepted them in July as the country reached the brink of bankruptcy.