Philbin, who helped guide the Packers to a 15-1 regular-season record and an NFC North title, will become the 10th coach in Dolphins history. The Dolphins confirmed the hiring in a news release and plan a news conference Saturday.
The hiring comes less than two weeks after Philbin's son drowned in a Wisconsin river. 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 and has been offensive coordinator since 2007. Coach Mike McCarthy called the plays, but Philbin put together the game plan.
"The Dolphins have a strong nucleus to build around, and working with everyone in the organization, I know that together we will return the team to its winning tradition," Philbin said in a statement.
"I have seen how much the fans in South Florida care about the Dolphins, and that passion is one reason why I'm really excited to be here. I'm looking forward to their support, and I can't wait to get started."
The Dolphins' top choice, Jeff Fisher, turned them down a week ago to become coach of the St. Louis Rams. Miami then conducted a second round of interviews this week with Philbin, Denver Broncos offensive coordinator Mike McCoy and Todd Bowles, Miami's 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.''
Ross fired Tony Sparano last month with three games to go in his fourth year as their coach. When the coaching search began, owner Stephen Ross said he would like to hire ''a young Don Shula'' and give the franchise some much-needed stability.
Instead he chose the 50-year-old Philbin, who has 28 years of coaching experience, all as an assistant, 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 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.
''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.
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.
The losing record was their third in a row, the franchise's longest such stretch since the 1960s. 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 and FOX NFL Sunday analyst Jimmy Johnson offered this tweet: ''Joe Philbin new Dolphin coach..good luck!''
The Associated Press and NewsCore contributed to this report