Jamison, 27, this week put pen to paper on a new three-year deal, tying him to Visy Park until the end of 2017.
One of seven free agents looming for the Blues at the start of the year, Jamison has joined Andrew Walker, Kade Simpson and Marc Murphy in committing to Carlton.
"The club's obviously shown terrific faith in me, it's now up to me to repay that over the next few years," Jamison told The Footy Show.
"I let my management deal with anything that came my way but I told them from the start it was always my intention to stay."
It is believed Gibbs' commitment to Carlton - to resist overtures to return home to South Australia - is imminent.
"I'm really, really confident Bryce will stay," Jamison said.
"Following, Simmo (Simpson), Murph (Murphy) and Walks (Walker) to all sign this year that will give him great confidence. I don't think it'll be too far away."
Jamison refused to write off the season as the Blues sit 13th heading into their bye weekend.
"Obviously the first month was disappointing, the last month we've gathered a little bit of momentum," he said.
"We can take that into the bye. We can certainly attack the second two-thirds of the year."
