Bendtner has scored 29 goals in 72 appearances for his country.
He scored 45 goals for Arsenal in 171 games between 2005 and 2014 and also had loan spells at Sunderland, Birmingham and Juventus during that period.
BBC Radio Nottingham’s Nottingham Forest correspondent Colin Fray
“Nicklas Bendtner is certainly a controversial figure and has his detractors, but Forest will be hoping that their marquee signing can combine with Britt Assombalonga up front and fire the club into top-six contention.
“He’s a player who’s proved he’s capable of scoring goals in his career – including in the Championship during his loan spell with Birmingham, when he was only 18 and was sent out by Arsenal to gain first-team experience. That spell apart, his entire career has been spent in the top flights in England, Italy and Germany, and he has a wealth of international experience with Denmark, too.
“So, as a free agent, you can see why Forest would be prepared to offer him a deal. At 6ft 4in tall, he’s likely to be handful for Championship defenders, and is the highest-profile signing of 12 this summer.”