No fee has been made public for the Republic of Ireland international who has yet to undergo a medical and finalise terms at Carrow Road.
But Bruce insists Norwich cleared the first hurdle in their attempts to sign the 23-year-old following Hull’s 0-0 draw with Hannover on Sunday.
“The two clubs have agreed a fee for Robbie,” he said. “We have given Robbie permission to go and speak to Norwich. I envisage that deal to go through.
“I want to thank Robbie for his efforts as he has been a terrific player for us. It’s sad to see him go but most people will understand that when you get relegated these things happen.
“When Norwich were relegated last season, we got Robert Snodgrass. They are doing the reverse this year and they have taken one of our good players. And he is a good player, and we wish him the best of luck.”
Brady will become Norwich’s third signing of the summer after Graham Dorrans and Youssouf Mulumbu, but manager Alex Neil is still hopeful of making further additions.
“I think there has been a lot of speculation surrounding us and players,” Neil said in a local newspaper.
“Rickie Lambert was tagged with us maybe two or three weeks ago now and then it went quiet and it crept back up again. At the moment it is just speculation.
“I think having added Graham Dorrans and Mulumbu if I could add another three or four I would be pleased. Over the course of the start of this week onwards we would like to hopefully do a couple more bits of business.”