The Canaries have confirmed Morison is poised to join on a three-year deal, for an undisclosed fee - subject to the relevant paperwork being completed.
He told canaries.co.uk: "Obviously I will be delighted to join Norwich when the deal is completed. They're a massive club who have earned the right to play in the Premier League and obviously as a player that's where you want to be.
"I had to work hard when I was playing non-league football but since then after joining Millwall it's been a rapid rise for me and now I've got the chance to play in the Premier League, to enjoy every minute of it and hopefully do everything we can to try to stay there.
"I know Andrew Crofts and Owain Tudur Jones from playing with them for Wales and I played against Russell Martin when he played against us for Scotland the other day. I know Zak from Millwall of course and Elliott Ward through his brother Darren, so I know a few of them already which is good."