The race will determine majority control of the court.
The top two-vote getters in the February primary will advance to the April election.
The race is officially nonpartisan, but candidates typically align along ideological lines. Current Justice Pat Roggensack is retiring rather than seek a third 10-year term. She is part of the four-justice conservative majority on the seven-member court.
Wisconsin Supreme Court
Kelly was appointed to the court in 2016 by then-Gov. Scott Walker, a Republican. Kelly served until 2020 when he was defeated by Jill Karofsky.
"If an activist were to win next April, Wisconsin's public policy would be imposed by four lawyers sitting in Madison instead of being adopted through our constitutional processes," Kelly said in a statement announcing his candidacy. "I won’t let that happen on my watch."
Protasiewicz's campaign manager, Alejandro Verdin, called Kelly a "radical right-wing extremist" with a partisan agenda and said he will contrast well with Protasiewicz.
Mitchell called Kelly a failed politician who would use the court for conservative activism.