Cunningham, who spent his entire 17-year playing career with the North-West outfit, was an assistant coach to Brown alongside Jamahl Lolesi.
Saints chairman Eamonn McManus told the club's official website: "Keiron is ready for this professionally and totally committed to the task ahead of him. He has been heavily involved in the success of this season and is ideally placed to carry it on for years to come.
"He is highly respected by the players. Not only does he understand our culture, he has been instrumental in its development since the inception of Super League. Everyone at the club is totally behind his appointment and enthused by it.
"The challenge ahead is an extremely one since the competition will be stronger next season and beyond. Keiron has the experience, ability and strength of personality to readily deal with it and will receive all of our support in so doing."
Cunningham's assistant coaches have not yet been named.