The oil-rich North African country has been wracked by bloody turmoil since a 2011 NATO-backed uprising killed long-time dictator Moamer Kadhafi, with multiple foreign powers now involved.
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The UN-recognised Government of National Accord (GNA) in Tripoli had been under attack since last April from forces loyal to strongman Khalifa Haftar, who is based in the east of the country.
Haftar's forces on January 6 captured the strategic coastal city of Sirte.
GNA head Fayez al-Sarraj on Monday called on Libyans to "turn the page on the past, reject discord and to close ranks to move towards stability and peace".
His comments came after a ceasefire began at midnight (Sunday 00:00 local time, Saturday 2200 GMT) in line with a joint call by Turkish President Recep Tayyip Erdogan and his Russian counterpart Vladimir Putin.
Since the start of the offensive against Tripoli, more than 280 civilians and about 2,000 fighters have been killed and 146,000 Libyans displaced, according to the UN.
The truce comes after a diplomatic offensive, led by Ankara and Moscow, which have established themselves as key players in Libya.
Ankara dispatched troops - in a training capacity, it said - to the GNA in January.
And Russia has been accused of backing pro-Haftar forces, which are supported by the United Arab Emirates, Saudi Arabia and Egypt, all regional rivals of Turkey.
Libya's head of High Council of State Khaled al-Mechri said the signing of the agreement in Moscow would pave the way for the revival of the political process.
The head of Russia's contact group to Tripoli, Lev Dengov, said the two rivals will have to determine in the Russian capital "the terms of the future settlement in Libya, including the possibility of signing an agreement on the ceasefire and its details".
He added he did not know if the two men would agree to meet directly.
Haftar will be accompanied by parliament speaker Aguila Salah, while Sarraj will go with speaker Mechri.
According to a Libyan source quoted by the Russian state news agency Ria Novosti, Khalifa Haftar has already arrived in Moscow.
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"They will have separate meetings with Russian officials and emissaries of the Turkish delegation, which is cooperating with Russia on this issue. Representatives of the United Arab Emirates and Egypt will probably be present as observers at the talks," said Dengov, quoted by Russian news agencies.
Turkish Foreign Minister Mevlut Cavusoglu and Defence Minister Hulusi Akar are also expected to arrive in Moscow on Monday.
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