Armed police were on guard as lorries said to be loaded with cash arrived at the central bank on Wednesday night.
Demonstrators took to the streets to protest against the bailout plan and strict capital controls.
The restrictions on the free movement of capital represent a profound breach of an EU principle, correspondents say.
Cyprus is the first eurozone member country to bring in capital controls.
Customers will be limited to withdrawing 300 euros ($383; £253) a day, to prevent everyone fleeing with their savings.
Depositors with over 100,000 euros will also see their savings taxed in exchange for bank shares as Cyprus seeks to raise 5.8bn euros to qualify for a 10bn-euro bailout from the European Union, European Central Bank and the International Monetary Fund, the so-called troika.
An earlier plan to tax small depositors was vetoed by the Cypriot parliament last week.
Correspondents say some fear a stampede as banks in Cyprus reopen between noon and 18:00 local time (10:00-16:00 GMT), nearly two weeks after they closed and progressively stricter limits were placed on withdrawals at cash machines.
Armed police are on guard and hundreds of staff from the private security firm G4S will be guarding bank branches and helping to transport money, said the AP news agency.