Wright takes over as Saints manager after spending the last 18 months as assistant to Steve Lomas, who left for Championship football with Millwall earlier this month despite guiding the team into the Europa League.
His first domestic match comes against a team currently in crisis, facing a 15-point deduction after revealing their intention to go into administration.
St Johnstone's first away trip takes them to Kilmarnock on August 10 and their first clash with champions Celtic takes place at Parkhead on September 21.
Boxing Day brings Celtic to McDiarmid Park with another Christmas home game on December 29 when Dundee United are the visitors.
Wright's men go on their travels on New Year's Day, going to Europa League qualifiers Motherwell who finished last season in second place.
The season splits on April 5 and St Johnstone's final scheduled fixture is a trip to Kilmarnock.