Syriza won 149 seats in the 300-seat parliament with its campaign of "Hope is coming!", leaving it just two seats short of an outright majority and in need of a coalition partner. The Independent Greeks, at odds with Syriza on many social issues like illegal immigration, won 13 seats.
The alliance is an unusual one. The parties, at the opposite end of the political spectrum, share only a mutual hatred of the 240-billion-euro bailout programme keeping Greece afloat at the price of budget cuts.
Stavros Theodorakis, leader of To Potami, a new centrist party once seen as a potential Syriza coalition partner, said he could not join a government that included the Independent Greeks, whom he called "far right" and "anti-European". But he said he would wait to see the government's programme before deciding whether to support a vote of confidence in parliament.
The tie-up suggests Tsipras will keep up his confrontational stance against Greece's creditors, who have dismissed his demands for a debt write-off and insisted the country needs reforms and austerity to get its finances back on track.
"At first sight this looks like a very strange marriage, but both parties share a strong opposition to austerity," said Diego Iscaro, an analyst at IHS Global Insight.