The Hammers agreed a £500,000 fee with Forest on Monday for the highly-rated striker after he turned down a new deal at the City Ground.
Forest decided to cash in on Harewood rather than risk losing him for nothing in the summer when his contract expires.
Hammers boss Alan Pardew was keen to bring in a new striker having lost on-loan signing Neil Mellor to injury and Jermain Defoe to suspension.
Harewood has signed in time to be available for Tuesday's trip to Wimbledon.
