The 18-year-old Austrian youth international had been on trial with the Clarets and will initially join up with the development squad.
Smith, who can also play in defence, joined Arsenal after leaving Chelsea two seasons ago.
"Hopefully in future years I can add something to the squad," he told the club website.
Find all the latest football transfers on our dedicated page.
Burnley have signed midfielder Renny Smith on a three-year contract following his release by Arsenal.