With voting underway under sunny skies in a tight race between Tsipras' Syriza party and the conservatives, the boyish leftwinger said: "The Greek people... Will take their future into their own hands... And seal the transition to a new era."
After a tumultuous seven months in office, Tsipras resigned in August and called snap elections, gambling crisis-weary Greek would give him a strong mandate despite being forced to continue with austerity measures.
Greek voters will elect "a fighting government" ready for the "confrontations necessary to move forward with reforms", said Tsipras, who in July agreed more punishing austerity for the nation in exchange for its third financial rescue in five years.
Over eight hours into the vote, the turnout seemed lower than the last election, AFP reporters said.
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Ballots close at 1600 GMT, when exit polls will be released, with first official results after 1800 GMT.
Over 9.8 million Greeks were registered to vote for a new government which, whoever wins, will face the tough task of pushing through painful new tax rises and pension reforms agreed under a three-year bailout deal adopted across-the-board by parliament last month.
Tsipras, who was elected in January on an anti-austerity platform, angered many in Greece by agreeing the deal for a new 86-billion-euro international rescue.