The deal was sealed less than two weeks after Philbin's 21-year-old son drowned in an icy Wisconsin river.
A person familiar with the decision confirmed the agreement to The Associated Press on condition of anonymity because the team hadn't made an announcement. The Dolphins are expected to hold a news conference Saturday.
Philbin, who has never been a head coach, first interviewed with the Dolphins on Jan. 7. The body of son Michael, one of Philbin's six children, was recovered the next day in Oshkosh.
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' 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, Miami's interim coach at the end of the season.
Instead he chose the 50-year-old Philbin, who has 28 years of coaching experience, including 19 years in college.
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.
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.
The losing season 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 long drought, former Miami coach Jimmy Johnson offered this tweet: "Joe Philbin new Dolphin coach..good luck!"