Brennan's agent Mark Curtis told the Nottingham Evening Post: "We have let Nottingham Forest know and Norwich are going to announce it in the next couple of days."
He also said how Forest and Paul Hart tried very hard to keep him but he has travelled to Carrow Road to finalise personal terms today.
He added: "There's certainly no bad feeling with Forest. He got on well with the players and staff."
Meanwhile Nottingham Forest have announced that around 10,500 season ticket holders have renewed for the forthcoming campaign.
Season tickets will go on general sale from Saturday 5 July.