The 28-year-old, who spent last season on loan at Championship side QPR, has signed a three-year deal at Carrow Road.
He leaves the Hammers after just three substitute appearances and 12 minutes of playing time in total following a £10m move from Preston North End in 2018.
Speaking to the club’s official website, Hugill said:
“Soon as I knew they were interested in taking me, it was a decision that I wanted to make quickly. To come here is brilliant for me and my family to get settled again, and hit the ground running.”