24-year-old Doig had been at Forest since the start of his career, making 76 starts in all competitions.
He had a loan spell at Northampton in the 2003/04 season and has signed a two-year deal at Sixfields.
Former Scottish international Jess was plagued by injury for much of his time at the City Ground after a move from Bradford in August 2002.
It has not been disclosed how long Jess has signed for.