Johnson is currently in his second term in that position.
He made the announcement Wednesday at the Democratic headquarters in Midland.
When asked about challenges he faces, Johnson says he's not worried because he has a great staff.
"Looking forward to continuing the work that we've started," Johnson said. "I've got a great group of ladies working in my office. Being in an elected position, we're only as good as the people that work with us. And I've got a great bunch of ladies in my office. And as I always say, I always brag, I've got the best staff of ladies in Midland County."