The 24-year-old, who scored 45 goals in 75 appearances for the Clarets, has penned a three-year contract at Loftus Road.
"Charlie's an out-and-out goalscorer and we're delighted to have him here," said QPR boss Harry Redknapp.
"He's scored goals wherever he has played throughout his career and I'm very confident he'll take his game to the next level with us.
"I've got no doubt that if we give him the right service he will score a lot of goals for us.
"He's young, he's hungry and he's up for the challenge of helping us get out of this division."
Austin, who has a strike rate of over one goal in every two games, was on the brink on a move to Hull City last month, only to fail a medical.
However, he believes he can achieve his Premier League ambitions with QPR.
"Harry spoke to me at length about the ambition of the club and the desire to return to the Premier League and that's where I want to be as well with QPR," he said.
"This is a really exciting time for me and I can't wait to pull on the QPR shirt for the first time.
"I'll come in, give my all and hopefully score the goals that ensure we have a memorable season."