Adebola has been strongly linked with a move to the KC Stadium in recent weeks and has now agreed a one-year contract with the Tigers.
He will add a physical presence to Nigel Pearson's attack next season and the 36-year-old is looking forward to a new challenge.
"I saw as an outsider what an impact the manager and his playing squad at Hull City had on the Championship last season and I want to be involved in the progress made here last season," Adebola told the club's official website.
"I'm really excited about taking on a new challenge and to get that opportunity at a big club such as Hull is great for me."
The former Crewe Alexandra and Coventry City forward scored five goals in 62 Championship appearances during his time at Forest and becomes Hull's third signing of the summer.
Tigers boss Pearson has also brought in Corry Evans and Joe Dudgeon from Manchester United, and is keen on deals for Jack Hobbs and Adebola's former Forest team-mate Paul McKenna.
Source: Team Talk
Source: Team Talk