Duterte's visit will end on October 5 and apart from Moscow, he is scheduled to visit Sochi, said the Philippines Foreign Affairs Ministry.
Philippines Foreign Affairs Assistant Secretary Amelita Aquino said Duterte and Putin "will discuss the state of our bilateral relations and how both sides can further enhance and expand our cooperation in various areas".
The two leaders would also exchange views on regional and global developments, Efe news reported.
Duterte called Putin his "favourite hero" when he was asked about his choice a few weeks before the US presidential election. He skirted the question and said he was "better off in saying that my favourite hero is Putin".
Duterte's visit comes a week after he announced that his country will not accept aid from 18 countries - the majority of them from Europe - who backed the UN Human Rights Council resolution, presented by Iceland, calling for probe over killings under the President's so-called war on drugs.
Apart from meeting with Putin, Duterte will also preside over a conference at the Moscow State Institute of International Relations, one of the most prestigious universities of the country, and will meet with some 7,000 members of the Philippines community living in Russia.
Some bilateral agreements will be signed during his visit. Duterte will also participate in Valdai Discussion Club on October 3 in Sochi.
This is Duterte's second visit to Moscow after his May 2017 trip which was cut short due to Marawi clashes, after some extremists occupied the city in the southern Philippines.
Duterte and Putin have met twice before: On the sidelines of the 2016 APEC summit in Peru and during the 2017 summit in Vietnam.
( With inputs from IANS )