Forest have paid in the region of £1.2 million for the 24-year-old, who was reportedly being tracked by several other Championship clubs, including Middlesbrough and Leicester.
Miller had been tipped to reunite with former boss Tony Mowbray, who played under for West Brom, at Middlesbrough.
Forest boss Steve McClaren told reporters: "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."
Miller is McClaren’s second forward signing in less than a week, having brought in former Olympiacos striker Matt Derbyshire after the ex-Blackburn man was told by the Greek giants he was free to find himself another club.
Forest fans will be welcoming the capture of another forward after seeing three strikers leave over the summer. Robert Earnshaw decided not to renew his contract at The City Ground before moving to Cardiff, while Dele Adebola joined Hull and Nathan Tyson switched to local rivals Derby.
The team has failed to score in either of their first two league games, going down 2-0 at Millwall and only managing a 0-0 draw in their season opener at home to Barnsley.