Neil moves to Carrow Road from Scottish Premiership outfit Hamilton Academical, who announced on Thursday that compensation had been agreed with Norwich.
The 33-year-old enjoyed notable success as player-manager at Hamilton, guiding the club to promotion last season and third place in the Scottish top flight this term.
He succeeds Neil Adams as Norwich boss after the latter resigned on Monday in the wake of an FA Cup third-round defeat to Preston North End.
Neil told his new club's official website: "I'm absolutely delighted to have the opportunity to manage a club of the stature of Norwich – it's an exciting challenge at a huge club and one that I'm looking forward to.
"I've watched a lot of Premier League and Championship football over the years and I've always been really impressed with Carrow Road and the Norwich fans and the way they get the place going when they get behind the team.
"It's a forward-thinking club with a fantastic infrastructure and big ambition, which matches my own ambitions.
"Of course I'm sad to leave Hamilton, a brilliant club which has been such a huge part of my life for so long. But when an opportunity as exciting as this with a club like Norwich comes your way, you take it.
"The aim now is simply to win as many games as possible and move Norwich City up the table."
Norwich currently sit seventh in the Championship, three points behind sixth-placed Brentford and 10 adrift of the second automatic promotion slot.
