Mueller has been out of the league since 2002
Incumbent staffers in the personnel department began meeting with Mueller, who has been out of the league since 2002, on Monday morning.
Mueller replaces general manager Rick Spielman, who resigned his post on Friday. He will have the same title, but by contract, not the same responsibilities as Spielman did.
First-year head coach Nick Saban, who still has control over all football decisions, prefers a personnel director. Mueller received a three-year contract, worth between $700,000-$800,000 per year.
"I am looking forward to my responsibilities with the Dolphins," Mueller said in a statement from the team. "This is one of the great franchises in the NFL with an unmatched tradition of success, and it's going to be special for me to be a part of that legacy."
Ironically, Mueller was one of several candidates who interviewed last year for the general manager opening. Owner Wayne Huizenga opted at the time, however, to stay in-house, and promoted Spielman to the post. It is not known when Mueller interviewed with Saban for the team's top personnel job.
"He is respected throughout the league and has a strong background in player personnel," Saban told The Associated Press. "He will help us in our continuing efforts to build a team that will not only achieve success, but sustain it on a long-term basis."
Saban had spoken earlier in the offseason with at least two potential candidates, Ruston Webster of Tampa Bay and Indianapolis' Chris Polian, but both men stayed with their incumbent teams and received promotions.
Mueller served as the executive vice president of football operations in Seattle between 1995-99, after 12 seasons in which he worked in the Seahawks' personnel department. He became the Saints general manager in 2000, and was voted the NFL's executive of the year that season, when New Orleans won the division title.
In May 2002, Mueller was abruptly dismissed by Saints owner Tom Benson. In the past three years, Mueller has interviewed for several prominent personnel positions.
Len Pasquarelli is a senior NFL writer for ESPN.com. Information from The Associated Press was used in this report. To check out Len's chat archive, click here .