Edgar, unhappy with the terms of a new contract offer at St James’s Park, had held talks with another club moving up from the Championship, Birmingham City.
But with discussions at St Andrews having stalled, Burnley boss Owen Coyle has moved in for the 22-year-old.
Edgar, raised in Canada and the son of former Newcastle goalkeeper Eddie, made 13 first-team starts for United, marking his home debut with a goal against Manchester United.