Johnston filed his letter of intent Friday with the Alaska Public Offices Commission, a first step needed to begin campaigning.
Wasilla is where Palin got her political start, first as a council member and then as mayor.
Earlier this month, Jones confirmed that Johnston planned to run for office as part of a reality TV show.
Johnston, 20, has had a prickly relationship with the Palin family since the birth of son Tripp and has sought to capitalize on his notoriety, posing for Playgirl and hitting the Hollywood circuit. He and Bristol Palin recently broke off a short-lived engagement.
The filing was first reported by TMZ.com.