The 21-year-old spent the majority of last season out on loan with Yeovil Town, where he made 41 appearances and scored three goals.
The towering defender's spell with The Glovers culminated in them winning promotion to the Championship by beating Brentford 2-1 in the League One play-off final at Wembley with Burn scoring what turned out to be the winning goal.
Standing 6ft 7in tall, Burn was born in Northumberland and began his professional career with Darlington in 2009.
His performances for The Quakers brought him to attention of Barclays Premier League outfit Fulham and he joined the Londoners at the end of the 2010/11 campaign before recently extending his stay at Craven Cottage with a new two-year deal
Burn told bcfc.com: "I'm really happy to have joined and I'm just looking to get back to pre-season training now. The history of this club was something that convinced me to join. Lee Clark, having played for Newcastle, is also somebody that I knew a lot about too and there's a lot of good players here. Now it's up to me to go and prove myself."
A full and exclusive BluesTV
interview with Burn will follow on bcfc.com later this week.
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