Tsipras is expected to use his second term to revive Greece's banks and its crippled economy, while demanding debt relief from creditors, an official told Reuters.
He was given a second chance by Greek voters, who looked through his acceptance of more austerity and economic reform in a bid to avert a "Grexit".
Read more: Germany concedes Greece needs debt relief
Syriza's stronger-than-expected win saw it secure 145 of 300 parliamentary seats, meaning the party needs just one small coalition partner to form a government. Some polls had suggested that Syriza's main rival, the conservative New Democracy, could clinch a win.
Syriza will turn to the small right-wing Independent Greeks party, which won 10 seats, and who it formed a coalition when the party first came to power in January.
Turnout for yesterday's vote was the lowest in Greece's history, at 55 per cent, signifcantly lower than the 63 per cent recorded at the last election in January.