Hobbs, 24, started 20 league games for the Tigers last season but was told by Bruce that he was surplus to requirements at the KC Stadium.
Nottingham Forest swooped to sign the former Liverpool defender on a deal that will initially be on loan, but with an option for a two-year deal thereafter.
The centre-back admitted his disappointment at being allowed to leave Hull, and has insisted that he will be looking to play in the Premier League during his time at the City Ground.
"Of course I would like to prove him [Bruce] wrong by getting to the Premier League and playing regularly," Hobbs said.
"I want to test myself at the highest level and was disappointed by Hull. It is the start of a new chapter and I am at a club who can do things.
"I just want to play in the Premier League and I'm playing somewhere I think I can achieve."
Nottingham Forest begin their Championship season with a home game against Huddersfield Town.