Police said they received a Crimestoppers tip on the truck the morning after the shooting and located it the next day in College Park.
They are still looking for the driver.
Deputy Chief Darrel Tolleson said police believe Thompson and the driver were trying to steal the tools from inside the construction workers truck.
Police said Thompson has an extensive criminal record and had only recently been released from custody before the shooting at Kroger. He is expected to make his first court appearance at 11 a.m. Friday.
Thompson has twice served in state prison, according to the Georgia Department of Corrections. Most recently, he was released from prison in January 2014 after serving about 17 months following a conviction for terroristic threats and acts, records showed. The same day he was released from prison, Thompson was booked into the Fulton County jail on other outstanding charges.
Thompson was also in prison from June 2009 until October 2010 on theft and obstruction charges. Sine 2008, Thompson has booked into the Fulton jail 13 times, records showed.
Richey, a father of four from the Birmingham suburb of Hayden, Ala., was employed by RGWilliams Construction, which set up a fund to help Richey’s family.
Kroger's Atlanta Division offered a $25,000 reward for information leading to the arrest and conviction of the person who shot and killed Richey.
The shooting happened at the grocery store known in the past as “Murder Kroger” because of previous crimes in the neighborhood.
Staff writer Alexis Stevens contributed to this article.