The Triple Crown is a "championship" consisting of three 500 Mile Super Speedway races on the IndyCar calendar.
The Triple Crown concept was first suggested by Pocono Raceway General Manager Bill Marvel in 1970.
Leonard said he hoped his sport's Triple Crown would soon be as prestigious as horse racing's established salute.
While running second at Pocono with six laps remaining, Johncock broke a gearbox and dashed his hopes to win all three races.
Domino's sponsorship of the award expired at the end of 1986 and the annual crowning of a champion based on points was discontinued.
"If you're gonna bring history back, the one thing that the fans wanted to see was the Triple Crown," IndyCar CEO Randy Bernard said.
Like the promotion in the 1980s, the Triple Crown revival carried cash bonuses, sponsored by Fuzzy's Ultra Premium Vodka.
When Pocono and Fontana were on the schedule together from 2013 to 2015, IndyCar did not officially announce a Triple Crown points champion.