Adams left former club Morecambe on Thursday after clinching promotion to League One via the play-offs.
The 45-year-old joins the Bantams having secured promotion out of League Two with two different teams in Morecambe and Plymouth, after previously enjoying success in Scotland with Ross County.
Speaking at a press conference as he was unveiled as Bradford’s new boss, Adams said: “The attraction is to come here and do well and try to get us promoted.
“I’m under no illusions of what this job entails, I enjoy working under that pressure. I know what I’m here to do.
“It is my job to identify what we need to get into a better position, walking into this football club is something I’ve enjoyed, the club have showed their vision of what they want and we’re looking to get ourselves moving.”
League Two Bradford have been without a boss since relieving joint managers Mark Trueman and Conor Sellars of their duties at the end of the 2020-21 season.
Bradford’s chief executive Ryan Sparks said: “I’m delighted to get the deal done. When we made the managerial change I made it clear that we didn’t want any new candidates.
“To appoint a promotion-winning manager is a clear statement of intent.
“When the fans come back they need to make sure they come back to a club they’re proud of.”