The hard-tackling midfielder joined the Canaries this month after leaving West Bromwich Albion following a six-and-a-half-year stay with the Baggies.
Mulumbu says one of the main reasons he decided to join Norwich was to work with impressive Scottish tactician Neil and he states that he certainly has not been let down.
The 28-year-old told the club's official website: "When I spoke with the club, I was really impressed and had no doubts about joining.
"The most important thing for a player is to be wanted by a coach, and he was the biggest reason behind me coming here. I'm looking forward to working with him and seeing how he wants me to play, because I'm a tactical player.
"He [Alex Neil] is a passionate man who likes football, and I wanted to come to a good team who work hard. I saw Graham [Dorrans] enjoyed his time here, so there were no doubts it was the right move for me.
"The best thing is to stay in the Premier League because everyone knows it's the best league in the world. Norwich were in the division two years ago, so we have experience in the squad which we'll need to have a good season."