Johnson becomes Paul Lambert’s fifth transfer of the summer following the 24-year-old’s contract at Elland Road coming to its end.
The Canaries new man made 107 appearances for the west Yorkshire side, scoring 17 goals in the process - including a memorable long-range effort against Arsenal in the FA Cup - and was part of the squad that achieved automatic promotion to the Championship back in the 2009-10 season.
On signing for the new Premier League side, Johnson told the club's website: ''I am over the moon really to get the chance to play in the Premier League with a big club like Norwich City and under a great manager who I have a lot of respect for.
''He [Lambert] has done a fantastic job since he arrived at Norwich and that was one of the main factors in me signing with the club.''
He added: ''I have dreamed of playing in the Premier League since I was younger and I feel I have done a lot of hard work to get there, coming up from the Ryman League now all the way to getting a chance in the Premier League, I just can't wait to get started.
''Norwich have already got some good players there and I have had some great battles with some of them over the past couple of years in my time with Leeds.
''They proved they were a good team by getting back-to-back promotions, and another deciding factor was to join a team that enjoys playing football and is hungry and has got that desire to succeed.
''I cannot wait to join up with the squad and meet everyone, get training and get a good pre-season under my belt.''