'Vampire Diaries' Star Zach Roerig -- I Got Custody of My Kid ... From Jailbird Baby Mama

Roerig was awarded custody last month in Georgia ... and a judge signed off on Zach making all future decisions for his daughter -- according to court docs.

We broke the story -- Roerig told the court he wanted child support from his ex back in July ... but it looks like he has since backed off the request.

Maybe it's cause he makes 30k a month from the TV show -- and she makes, well ... nothing.