"This does not constitute a victory for one party over another," Mikati told reporters. "This represents a gain for the Lebanese state and institutions.
"The dangers facing Lebanon required a courageous decision," he said.
Mikati last week had threatened to resign should his Hezbollah-dominated government refuse to fund the STL, a source of political tension in Lebanon since its creation.
"I don't want to be head of a government that fails to honour its international obligations and pulls the country out of the Arab and international community," Mikati said.
A government official said the $32 million (24 million euros) sent to the Netherlands-based STL were drawn from the prime minister's office's budget and as such did not need cabinet approval.
"This was a decision taken by the premier after consultations with the president," the official told AFP on condition of anonymity.
He said the funds were taken from the High Relief Council, which is under the auspices of the prime minister's office.
The move appeared to be a face-saving measure for Hezbollah and its allies as it did not require a cabinet vote.
The STL has indicted four Hezbollah operatives for murdering Hariri and 22 others in a car bomb blast in Beirut on February 14, 2005.
Hezbollah chief Hassan Nasrallah, who has denounced the court as part of a US-Israeli conspiracy, has steadfastly pushed for Lebanon to cut all ties with the tribunal.
The Shiite party, which is blacklisted as a terrorist organisation by Washington, has also vowed that those accused will never be found or handed over.
A party official contacted by AFP declined to comment.
The Western-backed opposition headed by Hariri's son and political heir, Saad Hariri, hailed Mikati's announcement, saying it amounted to tacit recognition of the court by Hezbollah and its allies.
"This is a clear and unequivocal victory for the current that never ceased to support the creation of the tribunal against another current that had denounced it as a US-Israeli tool," said Fares Soueid, secretary general of the coalition headed by Saad Hariri.
STL spokesman Marten Youssef welcomed the transfer of funds as did France and Washington, which also underlined that Lebanon's commitment to the court did not stop with the funding.
Ambassador Maura Connelly "noted that Lebanon's commitments... extend beyond the issue of funding alone and fulfilling these commitments are important indicators of the government's commitment to both Lebanon's interests and its international obligations," a US embassy statement said.
She was referring, among other things, to the STL's three-year mandate which is up for renewal in March and Lebanon's duty to track down and arrest those indicted for Hariri's murder.
Welcoming the move as well, US State Department deputy spokesman Mark Toner said: "The Special Tribunal's work represents a chance for Lebanon to move beyond its long history of impunity for political violence.
"The Lebanese authorities' support for, and cooperation with, the work of the Special Tribunal for Lebanon is a critical international commitment."
The French foreign ministry issued a statement also welcoming the transfer of funds and expressing hope that the tribunal will be able to carry out its work "in the best of conditions."
The Shiite Hezbollah, the most powerful military and political force in Lebanon, toppled the government of Saad Hariri in January after he refused to stop cooperation with the court.
Lebanon is responsible for meeting 49 percent of the STL's financing, which amounted to 32 million dollars this year.
Mikati in recent weeks had come under intense international pressure for Lebanon to uphold its duties towards the court, and STL president David Baragwanath visited the country to drive the message home.
The STL was created by a 2007 UN Security Council resolution at Lebanon's request. It opened its doors in 2009, tasked with trying those suspected of responsibility for Hariri's assassination.
It is the first international criminal tribunal with jurisdiction over terrorism offences and a mandate to try defendants in absentia if necessary.
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