ATLANTA — Two former Mississippi officials, including the head of the prison system, pleaded guilty to corruption charges on Wednesday amid a federal inquiry that rattled the state’s government and raised new questions about its use of private prisons.

The guilty pleas, entered in Federal District Court in Jackson, came nearly four months after the authorities announced a 49-count indictment that named Christopher B. Epps, the former commissioner of the Department of Corrections, and Cecil McCrory, a onetime state lawmaker who had become involved with the private prisons industry.

In the indictment, which formed the basis of Wednesday’s pleas, federal prosecutors accused the men of a scheme in which Mr. McCrory directed more than $1 million to Mr. Epps, including cash and mortgage payments, in exchange for lucrative state contracts.

Mr. Epps pleaded guilty on Wednesday to money laundering conspiracy and filing a false tax return. Mr. McCrory pleaded guilty to money laundering conspiracy.