19-year-old Jaanai, who operates as a striker, joins the Clarets from West Ham after signing a professional contract with the Premier League club in the last January transfer window.
The move to the Hammers followed his impressive form for League One side Peterborough United, a club whom he made his first team debut at just sixteen years of age.
The Northampton-born forward was on the books at Luton Town as a youngster before being snapped up by Posh at the age of fifteen and celebrated his seventeenth birthday by signing a three-year deal.
Injuries hampered his development but, with call-ups to the England under 18-squad and FA Cup appearances coming his way, earned a trial with West Ham and is known for his power and pace.
The club would like to officially welcome Jaanai to the Clarets and wish him an enjoyable and successful stay.