Earlier this year, the 91 year old was diagnosed with melanoma that spread to his brain.
Mr Carter received a round of targeted radiation and received doses of Keytruda, a newly approved auto-immune drug to help his body seek out any cancer cells appearing anywhere else in his body.
He shared his good news before giving a Sunday school lesson at Maranatha Baptist Church in his home town of Plains, Georgia.
Church leader Jill Stuckey said his announcement was greeted with applause.
"Our prayers have been answered," she said. "I can't think of a better Christmas present."