The 41-year-old, who also held talks with Ipswich Town over joining them, has signed a three-year deal at the City Ground.
"I know all about the expectation at the club and that we will be favourites to win promotion next season," he said.
"But we have to justify that rating. We will fight tooth and nail to produce the kind of football Forest fans want to see and hope it leads to success.
"I know it's a huge challenge but there will be a lot of managers out there envious of me right now."