Prosecutors say Judges Mark Ciavarella and Michael Conahan took the money in return for giving young offenders long sentences to serve in the centre.
The deal allowed PA Child Care LLC and a sister company to receive extra government funds, they say.
The judges in Luzerne County, Pennsylvania, have both been suspended.
They have pleaded guilty to honest services fraud and tax fraud.
The plea agreements provide for prison sentences of more than seven years.
Mr Conahan had shut down a county detention centre in 2002 and signed a deal with PA Child Care LLC to send offenders to its new centre, prosecutors say.
They said Mr Ciavarella sent youths to the detention centre while taking money in return, though the judge has specifically denied sending youths to jail for cash, the Associated Press news agency reports.
Campaigners have complained that Mr Ciavarella gave out overly harsh sentences for minor offenses.
A spokeswoman for the non-profit Juvenile Law Center said 1,000-2,000 juveniles who came before the judge between 2003 and 2006 received excessively harsh sentences.
Many of the children were first-time offenders and had no lawyers to defend them.
The judge sent a quarter of his juvenile defendants to detention centres from 2003 to 2006, compared with a state average of one in 10, the AP reported.
"Your statement that I have disgraced my judgeship is true," Mr Ciavarella wrote in a letter to the court, Reuters news agency reports.
"My actions have destroyed everything I worked to accomplish and I have only myself to blame."Mr Conahan made no comment.