The 41-year-old Leftist leader took a civil oath instead of a religious oath to "serve the laws, the constitution and the interests of Greek people" at a ceremony held at the Presidential Mansion in Athens, Xinhua reported.
Earlier on Monday, Tsipras formally received from President Prokopis Pavlopoulos the mandate to form the government for the second time in eight months.
Syriza won 35.5 per cent of votes and 145 seats in the next 300-member strong assembly, according to the final official results released by the interior ministry.
On Sunday night, a few hours after the closing of the ballots, Tsipras and Panos Kammenos, leader of the right-wing Independent Greeks party Anel, the junior partner in Tsipras's first government from January to August, announced their intention to renew the coalition partnership.
With the 10 seats Anel secured by garnering 3.7 of the votes, the new government will control 155 seats in the next chamber.