Rule was last December handed a two-year ban, back-dated to June, for his part in a cover-up after former Great Britain centre Martin Gleeson tested positive for the stimulant methylhexanaemine.
Rule was barred from from any involvement with rugby league players and the Rugby Football League say they have no objection to his appointment.
A spokesman said: "Widnes Vikings notified the RFL of the appointment and we immediately informed UK Anti-Doping.
"James Rule was suspended by a national anti-doping panel and under the terms of that suspension, he is not disqualified from fulfilling the role of chief executive."
Rule will take over from Julie Gaskell when she leaves the club over the next few weeks.
- Rugby Football League
- Martin Gleeson