UN special envoy Martin Kobler hailed the arrival of prime minister-designate Fayez al-Sarraj, urging a "peaceful and orderly handover of power" and praising his "exceptional personal courage".
Sarraj, a businessman named the government chief under a UN-brokered power-sharing deal in December, and several members of his cabinet arrived by sea with a naval escort.
Libya has had two rival administrations since mid-2014 when a militia alliance overran the capital, setting up its own authority and forcing the internationally recognised parliament to flee to the country's remote east.
But so far the two rival administrations have refused to cede power.
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A presidential council formed under the December deal confirmed on its Facebook page that Sarraj and several other members had "arrived safe and sound in Tripoli".
Kobler wrote on Twitter that their arrival "marks important step in #Libya democratic transition & path to peace, security and prosperity."
Sarraj and his cabinet had previously been blocked from entering the capital by the authorities there, who even closed the airspace several times to prevent them flying in.
After reaching Tripoli, Sarraj, who had been in Tunis yesterday, and his colleagues had lunch and met with officers at a naval base where they docked, a security official told AFP.