In a deep red district that Greene won by 29 points and Trump carried by almost 37 points two years ago, Fuller was on track to prevail by about 12 points with almost all votes counted.
Fuller insisted that his victory over Democratic candidate Shawn Harris in Georgia was a testimony to Trump's staying power.
“They couldn’t beat Donald Trump and they never will,” he told supporters in Ringgold, near the border with Tennessee. “And I will be on Capitol Hill as a warrior to have his back each and every day.”
Fuller will serve out the remaining months of Greene’s term, bolstering the party’s slim majority in the House, where Republicans control 217 seats to Democrats’ 214, with one independent.
He’ll have to face another Republican primary on May 19 to win a full two-year term, and could face a June 16 party runoff.
In another election held Tuesday, a Democratic-backed candidate for the Wisconsin Supreme Court won by double-digit margins, growing the liberal majority there.