The 24-year-old will commence a pre-agreed two-year contract at the end of the 2013-14 campaign that will keep him at the City Ground until the summer of 2016.
A former Liverpool trainee, Hobbs made 22 appearances for Hull last season as they clinched automatic promotion to the Premier League.
Forest boss Billy Davies said: "We are very pleased to welcome Jack to the club.
"He has for some time been recognised as one of the brightest defensive prospects outside the Premier League and I am delighted that we have been able to bring him in.
"To target players of his calibre is easy; the difficult part is making the deal happen.
"Not only do signings like this further signal our intentions this season, but they also highlight the hard work that is going on behind the scenes to ensure we are a force to be reckoned with.
"Things are slowly falling into place. There is still a lot of work to be done, but Jack is another piece in the jigsaw."