The move was expected after several government members including Azarov were elected to parliament on 28 October, obliging them to give up their ministerial roles.
Yanukovich told Azarov's government to stay on in an interim capacity, according to a decree published on the presidential website, and may well re-appoint it.
The 64-year-old Azarov is seen as a safe pair of hands who spent two and a half years trying to revive a debt-ridden economy that is struggling to recover from recession.
Growth rates have fallen again this year as demand shrank for Ukraine's main exports like steel, and further painful reforms seem inevitable.
"Yanukovich will not take risks and complicate things at a time when the world economy is in crisis," said political analyst Taras Berezovets.
The dour Azarov has also been at the forefront of tough - and so far unsuccessful - negotiations with Russia, Ukraine's main energy provider, to try to bring down the price of natural gas supplies, which the government says are way above market price and a huge drain on the economy.
Appointing someone else as prime minister, such as central bank chief Serhiy Arbuzov, with whom Yanukovich is personally close, could prove unwise and unpopular, commentators say.
As acting prime minister, Azarov is supposed to lead talks on a fresh lending agreement with an International Monetary Fund mission due to arrive in Kyiv on 7 December.
Whether or not he will keep his post thereafter will only become clear when the new parliament meets on 12 December.
Yanukovich's choice is likely to be approved by the assembly given that the Party of the Regions, which he and Azarov lead, says it is close to securing a majority in the chamber.
Ukraine says it hopes to use fresh IMF loans to repay $6.4 billion (€5 billion) of its debt to the Fund falling due next year. The IMF, in turn, insists that Kiev needs to raise gas and heating prices for households to cut the growing budget deficit.