Murray was recalled from a disastrous season-long loan with Watford to enable him to complete the move to Forest, where he will link up with former Albion manager Chris Hughton.
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.
Paying tribute to the 37-year-old back in September when he made the loan move to Watford, head coach Graham Potter said, “Glenn has been outstanding for this football club, a great pro and pleasure to work with. He quite rightly has earned legend status here."
Chairman Tony Bloom added, “His goals fired us into the Championship in time for our move to the Amex, and six years later into the Premier League.
“He also played a crucial role in helping the club retain its top-flight status during our first three years in the Premier League.
“As chairman, and on behalf of all Albion fans I would like to thank Glenn for all he has done for the club.”
Murray first joined Albion from Rochdale in January 2008 and became an instant hit with fans as he scored twice on his debut against Crewe Alexandra at Withdean.
His three-and-a-half-year spell culminated in promotion to the Championship, as Albion won the League One title in 2011, with Murray firing 22 goals as the club’s leading scorer.
That summer he moved to Crystal Palace, and he had subsequent spells with Reading and AFC Bournemouth, before he returned to the Albion in the summer of 2016.
In his first season back he topped the scoring charts again, this time netting 23 goals as the club won promotion to the Premier League.
He followed that with 14 and 15 goals in the next two seasons playing in the top flight.
Murray has played in the top six divisions of English football, across a pro career which began with his local club Carlisle United in 2004.
He also had a spell with Wilmington Hammerheads, having been spotted playing for Workington Reds in the Northern Premier League.
His Albion stats, across two spells are 285 games and 111 goals, making him second only to Tommy Cook (125) in the club’s all-time goalscorers list.