The single fraud charge carries a maximum penalty of 5 years in prison but under the plea agreement they agreed to serve 37 months, just a little over 3 years.
Bermingham, Darby and Mulgrew, each aged 45, were accused of conspiring with rogue Enron executives to defraud National Westminster Bank of $19 million, dividing $7 million among themselves.
NatWest is now owned by the Royal Bank of Scotland.
As part of their agreement with the U.S. government, the trio has to pay restitution to the Royal Bank of Scotland of $7.35 million.
The men, who were scheduled to go to trial in January, entered their pleas at a rearraignment hearing before U.S. District Judge Ewing Werlein.
Werlein must still approve the plea agreement and the recommended sentence. Sentencing is set for February.
The former bankers were arrested in 2004 and sent to the United States in July 2006 after a losing a lengthy and controversial extradition fight.