Instead of swearing on a Bible, as is customary, he took a non-religious oath.
Mr Tsipras's party, Syriza, scored a historic victory in Greece's election on Sunday but fell short of an outright majority in the 300-seat parliament, gaining 149 seats. While he moved quickly yesterday to arrange an awkward coalition with the Independent Greeks party, who won 13 seats, it immediately raised doubts over the longevity of the new government.
The only common ground between the two parties is their resentment of the austerity policies foisted on Greece for the past five years by the EU and International Monetary Fund (IMF) and their determination to renegotiate the country's 240 billion euro debt.
The parties admitted that they had profound differences. "Let us not beat about the bush, we are chalk and cheese," said Yanis Varoufakis, an economist from Syriza who is tipped to be the new finance minister. "It is a very strange alliance," said Vassilis Kostoulas, economics editor of Naftemporiki, a business newspaper.
"The only common characteristic between them is their opposition to the bail-out. For the rest, it will be chaos."
Mr Tsipras struck the deal with Panos Kammenos, the head of the Independent Greeks party, on his way to the presidential palace in Athens to be sworn in. "We have an uphill road ahead," he said to Karolos Papoulias, the Greek president.
Mr Kammenos, a former shipping minister, said his party would help steer Syriza through the challenges ahead. "The aim for all Greeks is to embark on a new day, with full sovereignty," he said.
A controversial figure, he claimed last month that Greek Jews paid fewer taxes than other citizens and were given preferential treatment.
His claims were dismissed by a Greek government official as "conspiracy theories, lies and slander" drawn from "the dark side of the internet". The Board of Jewish Communities in Greece called his words a "serious anti-Semitic act".
In an impassioned speech in 2012, Mr Kammenos vowed to repel the EU and the IMF, saying that Greece had been turned into a "laboratory animal" in an austerity experiment. "They have chosen the wrong laboratory animal for their experiment. They used the public debt as a means of control," he said.
There had been hopes outside Greece that Syriza might ally with a more moderate party such as To Potami (the River), which would have tempered its stance towards the EU and IMF. Mr Tsipras had reportedly reached out to them to discuss possible cooperation.
Instead, the opposite has happened and Greece now seems to be heading for confrontation with its eurozone partners, in particular Germany.
Angela Merkel wasted no time in telling Greece that it must honour its debts and continue with reforms. "In our view it is important for the new government to take action to foster Greece's continued economic recovery," said Steffen Seibert, the chancellor's spokesman. "That also means Greece sticking to its previous commitments." When it comes down to the hard business of bargaining, Mr Tsipras may find he has little room for manoeuvre.
If he fails to win significant concessions on reducing debt repayments, he could face a revolt from the Independent Greeks and the extreme Left of his own party, which represents up to 35 MPs.
That would probably bring down the government, forcing another election.
In his first few days as prime minister, the 40-year-old will find himself squeezed between the promises he made to Greeks about rolling back austerity and the perils of alienating the country's creditors.
"If Tsipras puts at risk Greece's position in the euro zone, it would be political suicide for Syriza and for him personally," said Mr Kostoulas.
