Several others declined invitations to interview as a replacement for Jeff Ireland, whose six-year stint as general manager ended Jan. 7 when he and owner Stephen Ross agreed to part ways.
Hickey has been with the Buccaneers for 18 seasons, including the past three as director of player personnel. He was their director of college scouting for six years.
He was not interviewed for Tampa Bay's GM job when it became open after this season. The Bucs won four division titles and one Super Bowl championship during his time with them, but went 28-52 over the past five years and had spotty draft results during that span.
Hickey was among eight candidates interviewed by Miami, with Ross aide Matt Higgins and executive vice president of football administration Dawn Aponte helping the owner with the screening process. The other finalist was Dolphins assistant general manager Brian Gaine, who worked under Ireland.
Some candidates and potential candidates expressed concern about the Dolphins' power structure, including the role of Aponte, who clashed with Ireland.
In a news release to announce the hiring, the Dolphins said Hickey will oversee all aspects of football operations and report directly to Ross. Coach Joe Philbin will continue to report directly to Ross as well, while Aponte's place in the chain of command wasn't spelled out.
Ross' loyalty to Philbin, who is 15-17 in two seasons with Miami, may have been a stumbling block for some candidates. In a statement, Ross cited Hickey's willingness to work with Philbin as a factor in the hiring.
"When we started the search, I outlined qualities that I was looking for in this position," Ross said. "These included a collaborative team-first person who can work with Joe, demonstrated player evaluation expertise, and someone who is open-minded and creative. Dennis fit all of these criteria."
The Titans' Dawson released a statement saying he had declined Miami's job offer.
"I felt Stephen is a great owner, passionate and wants to win, but the details of the offer didn't align with my vision," Dawson said. "I turned it down because it wasn't an ideal fit for my family and me."
So Ross turned to Hickey, who was interviewed for the first time 10 days into the search.
The protracted process reinforced Ross' reputation for having difficulty closing deals with the Dolphins. In the past, the New York real estate billionaire has unsuccessfully courted Peyton Manning, Jim Harbaugh and Jeff Fisher.
Hickey's task will be to upgrade the roster after Miami collapsed late in the season to blow a playoff berth and finish 8-8. The Dolphins haven't been above .500 since 2008, the longest such stretch in franchise history.
The tumultuous 2013 season included a locker-room bullying scandal that drew national scrutiny, and a report on the NFL investigation into the case will be released after the Super Bowl.
"The Dolphins certainly have talented players," Hickey said in a statement, "and I am eager to hit the ground running with our personnel and coaching staffs. We will all work together to construct a team that will make our organization and fans proud."
Hickey will be introduced at a news conference Tuesday.