The former Manchester United youth team player became Bournemouth’s third new singing of the summer, on a three-year deal, after signing for the Cherries back in May.
But as King was under 24 years of age, a compensation fee had to be paid to Rovers.
After spending three seasons at Ewood Park, the Norway International turned down the offer to stay at Blackburn, mentioning his lack of first-team football as the reason he wanted to depart, despite hitting the headlines last season for an FA Cup hat-trick against Stoke.
Blackburn have now agreed a compensation fee with Bournemouth, avoiding the need for a tribunal.
A statement on Blackburn’s website read: “Blackburn Rovers have reached an agreement with AFC Bournemouth in respect of compensation for former player Joshua King.
“Reaching this agreement means that a compensation fee will not now need to be set by the Professional Football Compensation Committee.”
Bournemouth confirmed the same agreement via a short statement on their website, adding that the fee would remain undisclosed.