Forest had been closely linked with the Welsh international, along with Derby County and Swansea City.
Wilson’s signing will be a real coup for Cardiff as the 23-year-old has already excelled in the league, when he scored 18 goals for Derby two seasons ago.
Last season he found the back of the net seven times for Bournemouth as they were relegated from the Premier League.
Liverpool were set to sell Wilson this summer for £ 15million, but no one was ready to go that high with Burnley unable to successfully haggle over fees.
With a sale to a Premier League side no longer an option after the first transfer deadline, Liverpool agreed to loan Wilson to a second tier club.
Forest is still looking to sign a winger with Anthony Knockaert from Fulham, who is reportedly close to joining.