The 28-year-old spent nine years at Arsenal, scoring 47 goals in 171 appearances although he made only 83 starts under manager Arsene Wenger.
"Please welcome Nicklas Bendtner who has joined #NFFC on a two-year deal," the club's chairman Fawaz Al-Hasawi said on Twitter.
Bendtner, who has also had loan spells with Sunderland, Birmingham City and Juventus, could face Arsenal when Forest meet the Premier League side in the League Cup third round later this month.
Forest, who became English champions in 1978 for the only time in their history a year after scraping into the top flight, achieved back-to-back European Cup triumphs in 1979 and 1980.
Forest have started the league campaign with three wins from their opening five games and are seventh in the standings.
(Reporting by Ian Rodricks in Bengaluru; editing by Ken Ferris)
