Gleason submitted the resignation to Town Manager Seth Lawless Tuesday. Gleason was first elected in 2005 and again in 2009.
"With reluctance, I have decided it is best, at least for now, that I step away from elected office," he wrote in a resignation letter.
In March, Gleason was arrested following a domestic dispute with his roommate. Police said they went to his home after getting a 911 call from a woman who said the men were fighting.
When officers arrived, they said they saw marijuana in plain view and Gleason was charged with drug possession.
In July, he was charged with DWI in a separate incident.