The Scot, who has won four promotions in his career - with the 45-year-old taking Morecambe to a historic promotion to League One on Monday - has signed a three-year deal with the club after City agreed compensation with the Shrimps.
Adams said: “Today is a great day for me. This a fantastic football club to come to and we have a big opportunity to try and earn promotion.
“Next season, my aim is to take us beyond this division and into Sky Bet League One. That is the pressure I put on myself, wherever I go, and I try to handle that pressure as well as I can.
“We have passionate supporters. The Bradford City fanbase is fantastic and was a big pull for me to come here. They want their manager to share the same passion, which is what I am here to do.
“We want to be a team that plays on the front foot and excites people when they come here. Hopefully, next season, we can get the supporters back to Valley Parade and have the place bouncing.
“Throughout my managerial career, it has always important to win, gain promotions and find yourselves in a higher position than you were the previous season.
“We all know Bradford City finished in the bottom half of the table last year. Now, we will aim to be in the promotion picture. That is what I am here to do.”
City’s chief executive officer, Ryan Sparks aded: “We are delighted to have secured Derek’s services, on the back of another promotion success for him.
“After we decided to make a managerial change last month, it was always our intention to bring Derek Adams to Valley Parade, and we are thrilled to have done so.
“Derek’s track record speaks for itself. He is a winner, works extremely hard, understands what it takes to build and sustain a successful side and has proven his ability to help teams at this level progress at an impressive rate.
“To claim his signature - given what he has achieved this season, and the interest in him from elsewhere - emphasises how special our football club is, and how attractive of a proposition it remains.
“Derek understands our vision, and fits into the culture we are trying to build, as we work towards achieving our on-field ambitions.
“I would like to take this opportunity to thank Graham Howse and Rod Taylor, Morecambe’s co-chairmen, for their understanding and cooperation over the past few days.
“They were aware of our interest in Derek for some time, though we mutually agreed to converse on the matter following their play-off campaign - which resulted in a remarkable and memorable moment for Morecambe Football Club.
“Derek’s achievements at Morecambe are unrivalled. He has left a lasting legacy, and we wish his former club the very best - ahead of their first campaign in English football’s third tier.
“We believe Derek’s appointment is a clear statement of our intent, and look forward to continuing to build a better Bradford City - with him in our dugout.”