The 21-year-old has enjoyed a good season for the Cottagers, making 15 Premier League appearances - 12 of which were starts - and scoring three goals.
However, with Ashkan Dejagah finding form following his summer arrival from Wolfsburg and Damien Duff's return to fitness, the Sweden international has dropped down a division to secure regular football.
The move to Burnley sees the former Liverpool man team up with Sean Dyche once again, his manager during a loan spell with Watford last season where he played 12 Championship matches.
"He is an exciting young prospect, and something different to what we have, which is important," Dyche told the club's official website. "He's dynamic and can mix up his game.
"He was with us at Watford last year and was then called back and went into Fulham's first team, which is obviously a good sign.
"He has started this season in the Premier League and got himself a couple of goals. We want to be progressive as a team and we have been waiting for the chance to freshen things and also allowed the group here to deliver what they can show us.
"We have been trying and Fulham have been aware of our interest for some time now. It's not just a kneejerk reaction; it has been in the pipeline for weeks.
"You have to wait for everything to align; our club, their club - and particularly the circumstances at a club you are trying to get a player from - and the individual.
"All those things have to align and it has done, so we are really pleased with that."
Fulham allowed another player to leave temporarily as Richard Peniket has signed for Blue Square Bet South side Farnborough, while James Musa's loan at Hereford United have been extended until April 4.