Pikiell, 48, led the Seawolves to the NCAA tournament for the first time in his 11 seasons as coach after winning the America East Conference title. He has a 190-155 record at Stony Brook and also guided the Seawolves to the NIT on three previous occasions.
The Seawolves were 24-6 this past season and lost to Kentucky in the first round of the NCAA tourney.
Pikiell led Stony Brook to six 20-win seasons in the last seven years and had the Seawolves in the conference championship game four times before finally winning this year. The former Connecticut point guard and assistant coach took over the program in 2005 and didn't have a winning season until 2008-09.
Pikiell will replace Eddie Jordan, who was 29-68 in his three-year tenure at Rutgers and 7-25 this season.
The Associated Press contributed to this report.