McKinnon was previously in charge of Brechin City, Raith Rovers, Dundee United and Morton before a spell with Falkirk, which ended in November.
The 49-year-old now takes over at the Ladbrokes League 2 side, who host Stenhousemuir at Hampden Park this weekend.
President Gerry Crawley told the Queen's Park website: "The club is delighted to bring someone with Ray’s experience to Hampden. Following the historic vote of our members on 14 November 2019 to transition to a professional model, Ray’s coaching experience at Scottish Championship level, together with his contacts throughout the game, will be invaluable."
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