The 19-year-old midfielder, who spent last season at Nottingham Forest and Middlesbrough, will play Premier League football for the first time with the Clarets until JanuaryBurnley have completed the signing of Chelsea midfielder Nathaniel Chalobah on loan until January.
The England Under-21 international spent last season at Nottingham Forest and Middlesbrough but is yet to make a Premier League appearance.
Chalobah, who can play in central midfield or at centre-back, is Burnley boss Sean Dyche's eighth signing since the Clarets finished as runners-up in the Championship to earn a place in the top flight.
Chalobah has also spent time on loan at Watford in the second tier, making 38 appearances and scoring five goals for the Hornets during the 2012-13 campaign.
Earlier reports on transfer deadline day had linked Burnley with a potential move for Manchester United midfielder Anderson.