The appointment to the number-two government position also makes Arbuzov a likely successor to Prime Minister Mykola Azarov.
The first major task of the new cabinet will be to secure a new bailout program from the International Monetary Fund.
An IMF mission is due to visit Ukraine late in January for what are expected to be tough talks on nailing down a new stand-by arrangement.
Ukraine needs to repay or refinance more than $9 billion debt falling due to foreign creditors in 2013, including $6.4 billion owed to the IMF which Ukraine hopes to refinance.
More often than not, the government and the central bank have worked together smoothly, avoiding public criticism of each other's policies. But Arbuzov is seen widely as closer to Yanukovich than his new boss Azarov.
"Financial and economic policy is now in the hands of the 'family'," said political analyst Volodymyr Fesenko, referring to Yanukovich's relatives and close associates.
Replacing Azarov with Arbuzov "looks almost inevitable next year. It is just a matter of time", he added.
Although Arbuzov comes across as media-shy and avoided open arguments with the government, official statements and leaked documents from the central bank indicated his opinions on economic matters sometimes differed from those of Azarov.
In June 2011, UNIAN news agency published a leaked letter in which Arbuzov told Azarov his government was losing credibility after refusing to carry out reforms recommended by the IMF.
The IMF has urged Kiev to pass on to ordinary Ukrainians more of the cost of the gas it buys at high prices from Russia, subsidies which are a large burden on the budget. Azarov has so far refused to take the unpopular step, although Kiev may have to become more flexible.
The government quit on December 3 after an October parliamentary election and its members have since served in an interim capacity, apart from Azarov who was reappointed on December 13.
Arbuzov, 36, will take over as first deputy prime minister from Valery Khoroshkovsky who quit the cabinet this month in protest at Azarov's re-appointment.
According to a separate decree issued by Yanukovich on Monday, Arbuzov will be in charge of economy, trade, state finances, agriculture and social policy.
Yanukovich's office said Yuri Kolobov, Arbuzov's former deputy at the central bank, would remain finance minister.
The president named former Energy Minister Yuri Boiko, former regional governor Olexander Vilkul and former Foreign Minister Kostyantyn Gryshchenko as deputy prime ministers.
It was not clear who would succeed Arbuzov at the central bank but last week Boris Pryhodko, head of treasury at state-run Oshchadny Bank, was named its new first deputy chairman.
Arbuzov emerged from relative obscurity to become a major figure in Kiev in September 2010 when he was named first deputy chairman of the central bank in a surprise reshuffle.
Less than four months later, Yanukovich named him central bank head, a position he has held since.
Before joining the central bank, Arbuzov, who was born and educated in Donetsk - Yanukovich's home region and power base - spent four months working at the state-owned Ukreximbank and his earlier career as a financier was in the private sector.
In particular, Arbuzov had worked at the Ukrainian Business Bank, a Donetsk-based lender which according to Ukrainian media is linked to Yanukovich's elder son Oleksandr.
Arbuzov's mother Valentina Arbuzova is the chief executive of the All-Ukrainian Development Bank, another private bank owned by Oleksandr Yanukovich.
Arbuzov reshuffled the central bank's senior management but largely continued the policies of the previous administration such as maintaining the hryvnia's peg to the dollar.
The two will need to work hard to revive Ukraine's economy, which shrank by 1.3 percent year on year in the third quarter as global demand for steel, the main Ukrainian export, fell.
(Additional reporting by Natalia Zinets; Editing by Tom Pfeiffer)