The matter had been set to go to a tribunal because of the Canada Under-21 international's age.
Edgar has made only one appearance for the Clarets so far, against Hartlepool in the Carling Cup.
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The Premier League's four representatives all face crucial matches in the final round of Champions League group games next month.
Arsenal were dealt a severe blow on Monday when it was revealed Francis Coquelin the injury the Frenchman picked up
For years, and years, and years, Tottenham Hotspur Football Club have fought tooth and nail to become a Champions League
Manchester United host PSV in the Champions League on Wednesday.
Juventus midfielder Claudio Marchisio is wary of a potential Manchester City backlash in Turin this week.