Mark Hughes has been out of football for three and a half years.
Hughes replaces Adams, who was sacked earlier this month after a run of nine wins in 37 games.
The first game in charge for Hughes will be the visit of Mansfield on Saturday, which is 11 points clear of the bottom of the table.
Hughes, who will take training for the first time on Friday, said: "I am really pleased to be here and am looking forward to the role, and the job in hand." It has been an exciting few days.
It is a little bit of a surprise that I have come in, but don't be put off by that!
I am here for a reason, so that people will come and watch and be proud to do so.
Since being out of management, I have missed the supporters coming in their numbers. I am looking forward to interacting with the crowd on the matchday.
From now until the end of the year, we want to finish strongly and see where that takes us.
We want to move the club and everyone with it forward, and hope we can have the success everyone wants.
It is Hughes' first job in management since he was sacked by Saints in December of last year, with his last game in charge a 2-2 draw against Manchester United.
The Welshman took an extended break after he was dismissed by Saints, but was eager to return to football management.
This is one of the most significant appointments in the history of Bradford, says the chief executive officer.
He said that Hughes inquired about the vacancies.
We are delighted to have secured Mark's services, and I am looking forward to working with him.
His record and stature in the game speaks for itself, and he has achieved a lot. He is a representative of the club&s desire to be successful.
Mark expressed an interest in becoming our manager and we are thrilled to be in a position to unveil him.
This is one of the most significant appointments in the history of the football club. Mark wants to make sure we fulfill our true potential.
Mark will be provided with the tools he needs in order to achieve our goals, be that in coaching, recruitment, sports science, medicine or any other area.
He has excelled in high-pressure situations in the past and is looking forward to the challenges ahead.
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