The 20-year-old Norwegian international became Henning Berg's first signing as Rovers boss after arriving on loan until January, with King impressed with what the manager had to say.
"I'm very excited to get the move to Blackburn," said the 20-year-old.
"They are a strong team in the championship and by coming here I want to help the team to get back into the Premier League where they should be.
"The manager was a big factor in coming here, he spoke to me, he told me about his plans and the way he wants his team to play it sounded right for me, I couldn't let that chance slip."
The Norwegian international paid close attention to Rovers in their previous outing against Peterborough United and was full of praise for striker Jordan Rhodes in the 4-1 win at London Road.
"I watched him against Peterborough and he impressed me and he looked great," added King.
"His finishing, his timing in the box, he's got an eye for a goal and I can't wait to play up front with him and to try and help him score more goals, and him help me too.
"I can't wait for the game on Saturday against Millwall."
King will wear squad number 15.
See Joshua King and the rest of the Rovers squad this coming Saturday when Millwall are the visitors to Ewood Park.
Tickets are on sale right now from £15 for Adults, £10 Seniors and £5 Juniors. Book online today at www.onerovers.co.uk