After having a bid rejected in December, Norwich kept tags on the former Stevenage forward and after having three bids knocked back last week, Norwich finally met Millwall’s valuation of the striker and the bid was accepted.
Morison has now penned a three year deal at Carrow Road, after passing a medical and agreeing personal terms.
Norwich boss Paul Lambert, who has already signed Everton forward James Vaughan, said: "Steve has been excellent for Millwall.
"It's really tough to step up to the Premier League, it's the best league in the world with the best players and stadia - and big crowds.
"We're glad Steve and James are here."
Millwall boss Kenny Jackett told the Southwark News: "Personally, I'd like to thank him for what he's done because he's done very well for the club over the last couple of seasons here.
"We haven't left it on bad terms and there are no issues at our end.
"We've tried very hard to keep Steve over the past six months, but we obviously have to look after the club along the way and make sure that the club's interests were in our thinking, especially in my position as the manager.
"So we wish Steve well in his future career and in the Premier League with Norwich."
