Johnson agreed to a judicial diversion program enabling the charges to be dropped if he pays court costs and successfully completes 363 days of unsupervised probation.
The Knoxville News-Sentinel first reported the news.
Johnson was charged with a DUI and cited for simple possession in July 2017. Police said Johnson had bloodshot eyes with alcohol on his breath and a marijuana cigarette next to him during a traffic stop.
The resolution comes 2-plus months after Knoxville jurors acquitted Johnson and former University of Tennessee teammate Michael Williams of aggravated rape charges stemming from a November 2014 incident. Johnson signed with the Broncos after the trial.