Tannenbaum will start his new job on Feb. 1, and both he and coach Joe Philbin will report directly to team ownership.
"Football's in my blood. I spent two years away from it, and I missed it dearly," Tannenbaum said in a conference call with reporters. "I missed the competition. I missed getting in a foxhole with a bunch of people that are committed to a cause. At the end of the day, I was very comfortable with that's who I am."
The 45-year-old has worked with the Dolphins as a consultant since August following 16 years with the Jets, the final seven of which were in a general manager capacity. Tannenbaum has a track record of being well-versed in salary-cap and contract-negotiation matters.
"I am excited that Mike Tannenbaum has joined the organization full time," Dolphins owner Stephen Ross said in a statement. "He is an experienced executive and leader that understands all facets of the sports landscape. During his time as a consultant this past season, I was able to see his impact first hand through his commitment and passion for innovation and using every possible avenue to find competitive edges."
The Dolphins hired Dennis Hickey to be their general manager last offseason. His notable moves included drafting offensive tackle Ja'Wuan James in the first round out of Tennessee and signing offensive tackle Branden Albert in free agency.
Tannenbaum said Hickey will keep final say on draft picks and players but it will be "a collaborative effort."
"I think there's good talent, and I think there's a really good foundation," Tannenbaum said. "I don't think this is a rebuild by any stretch."
The Dolphins finished 8-8 this past season, third in the AFC East.
Tannenbaum said the Dolphins are not far away from contending.
"Let's look at the team: Dennis Hickey and Joe Philbin have done a really good job," Tannenbaum said. "The cupboard is not bare by any stretch."
Tannenbaum is currently serving as an agent and, among other clients, represents Seattle Seahawks defensive coordinator Dan Quinn, who has had several interviews for teams regarding their head-coaching vacancies. However, he is transitioning to leave Priority Sports on Feb. 1 and no longer will represent Quinn. Rick Smith will run the coaching division, Tannenbaum said.
Tannenbaum will move to South Florida before he starts his new job on Feb. 1.
ESPN.com's Miami Dolphins reporter James Walker contributed to this report.