Quigg, a former WBA super-bantamweight champion, will move to Los Angeles to train at Roach's famous Wild Card gym.
"I have moved up to featherweight with the goal of becoming a two-weight world champion. I need a fresh challenge to help me grow," said Quigg, 28.
"This is an opportunity that I couldn't pass up."
I believe this move and change will take me to another level
American Roach trained former world champions Mike Tyson, Miguel Cotto and Oscar de la Hoya, and spent almost four years working with Quigg's fellow Briton Amir Khan.
Quigg made the step up to featherweight after losing his WBA title in a unification bout against Carl Frampton in February 2016 - his sole loss in 35 career fights.
His featherweight debut ended with a ninth-round stoppage of Jose Cayetano in December.
Discussing his split with Lancashire-based Gallagher after six years, Quigg said. "We have been a great team and achieved a lot and had some great wins together.
"I'd like to thank Joe for everything he has done for me; he is a tremendous coach and friend, which we will remain.
"Our first fight together was for the British title and I went on to become world champion under his guidance and for that I will be forever grateful."
British featherweight Scott Quigg is to team up with Manny Pacquiao's trainer Freddie Roach after confirming an "amicable" split from Joe Gallagher.