The shooting happened at a condominium on Pharr Road in Buckhead Saturday night.
Local media reported that 36-year-old Robert Bivines turned himself in on Monday.
Thornton exited the apartment and exchanged a few words with Bivines before the fatal shooting, witnesses told investigators after the incident.
The men got into an argument before authorities say the driver shot his customer several times. "We have been working with the Atlanta Police Department, and the driver can no longer access the app".More news: Guardiola looks to another Cup after Wigan upset
Bivines' attorney, Jackie Patterson, told WSB-TV his client "had no choice but to defend himself" when the man became irate and aggressive over his order. Bivines, who was employed for the food delivery service for about a week, was arrested on February 19 on charges stemming from the murder.
Patterson said Bivines then saw Thornton turn around and reach into his jacket pocket. NBC's 11Alive reports that the victim, who had recently graduated Morehouse College with a degree in political science, was his mother's only son, whose husband passed away three years earlier.
He will have a first appearance before a judge on Tuesday.
An unnamed UberEATS driver is wanted by police after allegedly killing his own customer.
"We are shocked and saddened by this news", the spokesman said.