Static, aka Virgil Hawkins, first appeared in Static #1 (1993), published by Milestone Media. Like most superpowered people in Dakota, he got his powers in an event called the Big Bang, but whereas the others were generally gang members and criminals, he was a smart kid who just happened to be in the wrong place at the wrong time.
In 2000, Milestone Media adapted Static into a show on the Kids' WB called Static Shock. As it was a Saturday morning cartoon, they made it more kid-friendly and a little brighter, which included a more standard superhero costume for Static:
In 2001, Milestone and DC published a miniseries called Static Shock: Rebirth of the Cool. Although a sequel to the original Static series, this time he wore his animated outfit. The costume actually first appeared in printed form on the cover of Static Shock: Trial by Fire, which was published in anticipation of the animated series, it does not appear in the book itself.
Static Shock season 3 (2003) saw a number of changes to the show, including Static's outfit, as seen below:
In December 2008, Static made his first appearance in DC Comics proper, in Terror Titans #3, wearing his season 3 (and 4) outfit. This signaled the merging of the Milestone and DC universes, a move which had already happened in the DC Animated Universe during Static Shock season 2.
The DC/Milestone merger survived the New 52 and Static was one of the first 52 series launched, but it only lasted eight issues. Milestone Media has since announced plans to relaunch, and what that means for their characters appearing in the DC universe remains to be seen.