The Louisville Courtier Journal reported Williams will not have to serve jail time.
The newspaper reported that two other charges -- driving without a license and felony tampering with physical evidence -- were dropped as part of a plea agreement.
An initial sentence of 120 days in jail was waived as long as Williams follows the conditions of his release.
He was ordered to undergo a substance-abuse evaluation to determine if he has a drug problem and to obey any recommendation that comes from that evaluation.
Williams, a linebacker for the Cardinals, was kicked off the team Sept. 27 following his arrest.