The Dolphins are planning to promote defensive pass game coordinator/cornerbacks coach Josh Boyer to defensive coordinator to replace Graham.
In plucking Graham from Miami, new Giants head coach Joe Judge sought out a familiar face in one of his first moves to fill out his staff. Judge was on the staff with Graham in New England from 2012 to '15.
It's also a return home of sorts for Graham, who was the Giants' defensive line coach in 2016 and '17.
Graham, who is close with Dolphins head coach Brian Flores, leaves Miami after just one season as the defensive play-caller. The Dolphins will also bring in a new offensive coordinator for the second consecutive season, after Flores fired Chad O'Shea and lured Chan Gailey out of retirement to fill that role two weeks ago.
The Dolphins finished 30th in total defense in 2019 with a bare-bones roster in the early steps of a rebuild. But the Giants have hope that Graham can help improve a defense that finished 25th this past season under previous defensive coordinator James Bettcher. The Giants didn't have a single Pro Bowl player, and only two teams had less money invested in the defensive side of the ball.
"That's great," one player who has worked extensively with Graham said after hearing about the hiring. "He's a good coach."
Graham, a Yale graduate who once had dreams of working for the CIA, takes over a young Giants defense that started nine first- or second-year players this season. They had five rookies start at different points throughout the season, including three in the secondary at the same time.
The Dolphins, who had to approve the interview and hire for a lateral move, saw a lot of promise in Boyer and believe he can flourish in his new role. Boyer has a reputation of identifying and developing hidden defensive talent, with success stories like Titans cornerback Malcolm Butler, Patriots cornerbacks J.C. Jackson and Jonathan Jones and Dolphins cornerback Nik Needham.
Boyer, who also has a strong relationship with Flores, played a key role in a Dolphins defense that finished tied for 12th in interceptions despite seeing four of its five Week 1 secondary starters finish the season on injured reserve or traded.
NFL Network was first to report the defensive coordinator moves.
ESPN Giants reporter Jordan Raanan contributed to this report.