The 22-year-old has agreed a short-term deal at Turf Moor, hoping to prove over the next few months that he is worthy of a long-term stay.
And the Championship club have high hopes of the Millfield-born forward, having tracked him for more than a year in Under-21 Development games.
Noble had several longer term offers on the table but felt the Burnley opportunity was just too good to turn down.