The left-back, from Dublin, has signed a two-year deal.
Burke, 18, has been a mainstay of the Blues Under-23s side.
And his tough-tackling nature, allied to a sweet left foot, has been one of the standout features of the Development Squad.
An Ireland Under-19 international, Burke came to Blues via St. Patrick's Athletic in July 2017 after a successful trial.
He made his Development Squad debut on the day he turned 17 and helped lead Blues to the FA Youth Cup Semi-Finals two seasons ago.
He made 29 appearances for the Under-23s last season, scoring once, as they finished runners-up in the PDL North and Play-Offs.