Dee will oversee business development of the team and stadium, the Dolphins said Sunday. He'll be in charge of marketing the team and new projects at the stadium.
The Dolphins said there will be no change in the role of Bill Parcells, who will continue to oversee football operations and report directly to owner Stephen Ross.
Dee spent 14 years in major league baseball, including the past five as chief operating officer of the Red Sox while they consistently set records for attendance and revenue growth. He oversaw business operations and such improvements as the Green Monster seats, and brought concerts to Fenway Park. He was also president of Fenway Sports Group, a wholly-owned subsidiary of New England Sports Ventures, the parent company of the Red Sox.
Dee earlier spent eight seasons with the San Diego Padres.
"I'm thrilled to be able to add someone of Mike's background and expertise to our organization," Ross said. "His accomplishments with the Red Sox greatly expanded their business footprint and amplified the team's standing as one of the premier franchises in professional sports."
Dee said the Dolphins' business operation will be committed to providing sufficient resources for them to compete for a Super Bowl title every year.
"The Dolphins have a great history, a great established brand, but our goal is to fill Dolphin Stadium game in and game out," Dee said. "Everybody is a Dolphin fan, from our point of view. We want people coming back to the stadium time and time again, and we intend to make that experience the best that the NFL has to offer."
Ross completed his purchase of the Dolphins in January and has said he wants to rebrand the franchise and upgrade the fan experience at games. Joe Bailey, who had overseen the business operation as chief executive officer for Dolphins Enterprises, remains with the organization, but his future is uncertain.
Red Sox owner John Henry said Dee's departure was a "great loss."
"His rare combination of imagination and ingenuity has helped this franchise reach historic milestones on and off the field," Henry said. "His work with Fenway Sports Group and Roush Fenway Racing were critical to the growth and success of those entities, and his work with every facet of NESV set high standards of excellence across the board."