Rovers have paid an undisclosed fee for the 20-year-old, who has signed a contract until 2015.
"I've enjoyed my time here, we've a great group of lads and I think I've settled in well," King told the club website.
"I'm happy to be here and I'm really looking forward to the next two and a half years that I've signed for.
"Everybody has made me so welcome here. I feel comfortable here and I'm happy to make the deal permanent."