Forest have reportedly paid an initial £1.2million for the highly-rated striker.
The 24-year-old has signed a three-year contract with Miller.
Forest boss Steve McClaren told the club’s official website: “Ishmael is still a young player but has loads of experience and a lot to prove.
“He wants to play, which is why he’s coming to Forest. He’s the type of player we want at the club – he’s young and ambitious and fits the criteria perfectly.”