The deal was sealed less than two weeks after Philbin's 21-year-old son drowned in an icy Wisconsin river. The Dolphins confirmed the hiring in a news release and plan a news conference Saturday.
Philbin, who has never been a head coach, first interviewed with Miami on Jan. 7. The body of son Michael, one of Philbin's six children, was recovered the next day in Oshkosh.
After spending a week away from the Packers, Philbin rejoined the team last Sunday for its divisional playoff loss to the New York Giants.
Philbin has been with Green Bay since 2003, serving as offensive coordinator since 2007. Coach Mike McCarthy called the plays, but Philbin put together the game plan for one of the NFL's most prolific offenses.
The Dolphins' top choice, Jeff Fisher, turned them down a week ago to become coach of the St. Louis Rams. Miami owner Stephen Ross and general manager Jeff Ireland then conducted a second round of interviews this week with Philbin, Denver Broncos offensive coordinator Mike McCoy and Todd Bowles, the Dolphins' interim coach at the end of the season.
"Joe has all the attributes that we were looking for when we started this process," Ross said in a statement. "Jeff Ireland and I felt Joe was the right choice to bring the Dolphins back to the success we enjoyed in the past."
The Dolphins are coming off a third consecutive losing season, their longest such stretch since the 1960s. Even so, Philbin called them "one of the premier franchises in professional sports."
"The Dolphins have a strong nucleus to build around," he said in a statement. "And working with everyone in the organization, I know that together we will return the team to its winning tradition."
Ross fired Tony Sparano last month with three games to go in his fourth year as the Dolphins' coach. When the search for a new coach began, Ross said he would like to give the franchise much-needed stability by hiring "a young Don Shula."
Instead he chose the 50-year-old Philbin, who has 28 years of coaching experience, including 19 years in college.
With Philbin's help, the Packers have ranked in the top 10 in the NFL in yardage each of the past five seasons, including third in 2011. A year ago they won the Super Bowl.
"A huge congratulations to Joe Philbin," Green Bay tight end Jermichael Finley tweeted. "No one deserves it more than this guy. The Pack will miss him!"
The hiring might give the Dolphins an edge if they decide to pursue Packers backup quarterback Matt Flynn, who becomes a free agent this offseason. Flynn set Packers records with 480 yards passing and six touchdowns in their regular-season finale. Philbin played a major role in the development of Flynn and Pro Bowl quarterback Aaron Rodgers.
"Worked five years with Joe Philbin," former Packers executive Andrew Brandt tweeted. "Calm, cerebral, humble and a skilled offensive mind. His style will resonate with players."
Assistants becoming first-time NFL head coaches have had mixed results in recent years. The group includes the Ravens' John Harbaugh, the Saints' Sean Peyton and the Steelers' Mike Tomlin, but also three coaches recently fired -- Jim Caldwell by the Colts, Todd Haley by the Chiefs and Steve Spagnuolo by the Rams.
Before joining the Packers, Philbin was Iowa's offensive line coach for four years. The former small-college tight end has been an offensive coordinator at Harvard, Northeastern and Allegheny College.
Philbin becomes the seventh coach in the past eight years for the Dolphins, who went 6-10 this season and missed the playoffs for the ninth time in the past decade. It has been 19 years since they reached the AFC championship game, 27 years since they reached the Super Bowl and 38 years since they won an NFL title.
Perhaps mindful of the drought, former Miami coach Jimmy Johnson offered this tweet: "Joe Philbin new Dolphin coach..good luck!"
Philbin will now begin assembling a staff. Bowles might remain as a replacement for defensive coordinator Mike Nolan, who took the same job this week with the Atlanta Falcons.