He moved to Turf Moor in the summer on a four-year deal, but the clubs were unable to reach agreement on the transfer fee.
The matter had been set to go to a tribunal because of the Canada Under-21 international's age.
While Newcastle have brought in 'loan' signings to fill the full-back position, Edgar has made only one appearance for the Clarets so far, against Hartlepool in the Carling Cup.