David Drumm will now remain in custody in Boston until his hearing in federal court on Tuesday.
He moved to the US in 2009, the same year Anglo Irish collapsed and was bailed out by Irish taxpayers.
Mr Drumm, who ran Anglo Irish Bank from 2005 to 2008, 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 (Â£8.34m).
It was alleged during the 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.
It was reported in January that the Republic of Ireland was seeking his extradition.
Bailing out the bank cost Irish taxpayers around 30 billion euros (Â£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.
The former boss of Anglo Irish Bank has been arrested on an extradition warrant, the US Attorney's Office in Massachusetts says.