Murray joined Hornets on a season long loan deal last summer but struggled for game time.
His loan was terminated by Watford and the 37-year-old striker had been training alone while searching for a new club.
A move to Queens Park Rangers fell through earlier this transfer window as they signed their former striker Charlie Austin instead.
Murray though has finally found his escape route from Vicarage Road is now set to link up with his old Brighton boss Hughton, who is currently in charge at the City Ground.
It is understood to be a permanent deal, rather than a loan, and the move will officially end Murray's association with Brighton.
Murray made 285 appearances for Albion and scored 111 goals. His best season was in 2016-17, under Hughton, as he netted 23 goals in the Championship as the Seagulls gained promotion to the Premier League.
Forest are currently struggling in the Championship and are just three points above the relegation zone.