The party secured 149 out of 300 seats, official results from the polling stations showed.
A total of seven parties have passed the 3-percent threshold needed to enter the Greek parliament. Current Prime Minister Antonis Samaras' conservative New Democracy party garnered 27.81 percent, receiving 76 parliamentary seats.
Meanwhile, Syriza party leader Alexis Tsipras has been sworn in as new prime minister in a ceremony attended by Greek President Karolos Papoulias.
"I want to say, simply, that from this moment, there is a government," Panos Kammenos, the Independent Greeks leader, was quoted as saying by The Guardian on Monday after a meeting with Syriza.
The 149 seats gained by the Radical Coalition of the Left fell just two short of an absolute majority. The anti-austerity party is in discussions with other parties that have surpassed the 3-percent election hurdle for a possible coalition.
In his election campaign, Syriza's Tsipras pledged to put an end to the widely unpopular austerity measures imposed by EU bankers, including severe budget cuts and tax hikes. On speculations about Greece exiting the eurozone, Tsipras made assurances that his party did not intend to take Greece out of the currency bloc.
