Mr Drumm, who resigned in December 2008 as the bank was collapsing, was brought before Dublin District Court on Monday to be charged with 33 offences.
They include false accounting linked to transactions worth 7bn euros (£5.4bn).
He was arrested in the early hours of Monday after arriving at Dublin Airport on an overnight flight from Boston.
Gardaí (Irish police) accompanied the former chief executive on the transatlantic flight and shortly after landing he was brought to a Dublin police station, and then escorted to the court.
The hearing was told that Mr Drumm made no reply when police officers put the charges to him at the station.
Sixteen of the charges relate to the alleged provision of unlawful financial assistance to 16 wealthy investors, in a bid to prop up Anglo's share price before the collapse.
Mr Drumm moved to the US in 2009, the same year Anglo Irish Bank had to be bailed out by Irish taxpayers.
Police objected to his bail application, claiming the accused is a potential flight risk.
A sergeant told the court police believed Mr Drumm had the capacity to flee the jurisdiction and seemed to have access to large sums of money when required, despite owing millions in debts.
A prosecution lawyer told the court the accused had fought tooth and nail against his extradition from Boston and had been leading the authorities a "merry dance" during the process.
However, Mr Drumm's solicitor said his client had offered to surrender his passport, be tagged and sign on twice daily at his local police station.
The defence lawyer added that the accused had offered to provide a "relatively large" amount of cash and had several family members who were willing to "put their houses on the line" so he could be granted bail.
The judge granted bail on Mr Drumm's own bond of 50,000 euros (£39,000) and two independent sureties of 50,000 euros.
Mr Drumm ran Anglo Irish Bank from 2005 to 2008 and subsequently filed for bankruptcy in the US.
However, the bankruptcy bid failed and a Boston court ruled that he could be held liable for debts of 10.5m euros (£8.34m).
It was alleged during the bankruptcy case that the 48-year-old former bank boss secretly transferred money and assets to his wife, so they could not be seized during bankruptcy proceedings.
Authorities in the Republic of Ireland issued an extradition request last year and he was arrested at his American home in October.
At a hearing in Boston last month, Mr Drumm agreed to return to the Republic of Ireland as soon as possible.
Bailing out the bank cost Irish taxpayers about 30bn euros (£22bn: $34bn), close to one-fifth of annual output.
Its downfall played a large role in the collapse of the Irish economy in 2008 and the ensuing bailout from its eurozone partners two years later.
David Drumm, former boss of the Anglo Irish Bank, has been granted bail by an Irish court after he was extradited from the US to face fraud charges.