Brellier, a former charge of City's assistant boss Jim Duffy, has signed a two-year deal at Carrow Road after leaving Heart of Midlothian on a free transfer.
The 25-year-old began his career at Montpellier before joining Inter Milan in 2000. He later had loan spells at Lecco and Legano before joining Hearts, then managed by George Burley, in 2005.
A defensive midfielder, Brellier is described as 'no nonsense' and has earned the nickname 'Le Juge'. He has amassed a total of 22 yellow cards and two red cards in two seasons at Tynecastle.