Monroe has been suspended indefinitely since being arrested on a charge of drunken driving in November. On Friday, the DWI charge was dropped as part of a plea agreement in which he pleaded guilty to obstruction of a passageway. He received deferred adjudication.
The story was first reported by the Austin American-Statesman.
The final hurdle in clearing his status was a meeting with coach Mack Brown, which was expected over the weekend or early in the week.
Monroe set a school record by returning two kickoffs for touchdowns this season. He also had 110 yards rushing on 20 carries. He's missed the last three games.