The United Nations called on the country's lawmakers to endorse the new administration, after less than half of members of parliament signed up to the agreement.
The unity government, headed by businessman Fayez al-Sarraj, comprises 32 ministers, the administration announced on its Facebook page.
"I congratulate Libyan people & Presidency Council on formation of Govt. of National Accord," UN envoy Martin Kobler wrote on Twitter.
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Libya has been in chaos since the 2011 ouster of longtime dictator Moamer Kadhafi.
The country has two rival parliaments and administrations -- in the militia-held capital and in eastern Libya -- as well as the new unity government.
On December 17, under UN guidance, around 80 of 188 lawmakers from Libya's internationally recognised parliament and 50 of 136 members of the Tripoli-based General National Congress signed the deal.
World powers are pressing all sides in the conflict to accept the power-sharing deal, which has been given added urgency by fears that jihadists in Libya are building a new stronghold on Europe's doorstep.