The Devils will get 26-year-old defenseman Dalton Prout, while Dallas lands 21-year-old defenseman Dillon Heatherington.
The 31-year-old Quincey had four goals and eight assists in his only season with the Devils. He has played eight years with the Red Wings, three with the Avalanche and one with the Kings.
He is an unrestricted free agent after this season who carries a $1.25 million cap hit.
Korpikoski, 30, had eight goals and 12 assists in his first season for Dallas. He has played for five teams in his nine-year career.
He signed a one-year, $1 million deal with the Stars before this season.