The 29-year-old former Preston, QPR and West Ham hitman is an experienced Championship performer and provides Baggies boss Valerien Ismael with another option up front.
Hugill scored five goals in 31 appearances for the Canaries last season, though only seven of those were starts.
“Jordan has the player profile we have been looking for and is the type of striker we needed,” said Ismael. “I think with his experience, his mentality and his work ethic, he will suit us perfectly.
“We took our time to make the right decision and, after our first discussion with Jordan, we felt that he’s the right player for us. He was immediately committed to Albion and to our way to work and play. It’s exactly what we wanted; for a player to want to come here to help make us successful. I also think this is the right place for him.
“Jordan will allow us to be more adaptable as a team. We will have some games that are different and we will need more physicality in the box, making life difficult for the opponent’s centre-backs.
“He will help us link-up play and he will give us a different style, which is important in the Championship. He is strong in the air which will help us and he has a presence to win important duels.
“His skill and his experience will help him to score a lot of goals for us. He is able to score from open play and set-pieces.
“I think we saw already in our first few games that we have had a lot of crosses into the box and it is important we have a striker in the area who is able to win those headers.”