In September, FC Goa began their preparation for the ISL in style - winning their first ever Durand Cup.
Nawaz was a key member of FC Goa's set-up after playing an important role in the club's successful seasons in 2018-19 and 2019-20.
The 33-year-old centre-back has made 14 appearances for the Indian national team and his experience will be handy for the Kolakata- based side.
According to media reports, the Australian put pen to paper on a one-year contract with the club after completing the formalities on Tuesday.
SC East Bengal announced the signing of Indian international Amarkit Singh Kiyam from FC Goa on loan.
The 23-year-old Indian managed to score an impressive four goals in just 131 minutes of game time for FC Goa in the previous ISL season.
The youngster joined FC Goa last summer on a permanent move from Shillong Lajong but will go out on loan this season.
The 21-year-old has put pen to paper on a long-term contract after passing medical and agreeing personal terms.
The 33-year-old forward, who has played in multiple European clubs, has penned a one-year deal with the Gaurs.
The 22-year-old defender is coming off a season where he helped Sporting Clube de Goa to the Goa Pro League title.