The former Preston and West Ham striker joined the Canaries ahead of the 2020-21 season and scored five goals as they were promoted back to the top flight.
He will now look to achieve the same as West Brom target an immediate return to the Premier League and manager Valerien Ismael believes the 29-year-old is the ideal striker for his side.
"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," Ismael told the club website.
"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.
"I think with his experience, his mentality and his work ethic, he will suit us perfectly."
Hugill added: "Coming here was the best option I could have possibly picked.
"You look at the size of the club and everything else that comes with the name West Bromwich Albion, it was something I just felt I had to be a part of.
"I'm delighted to be here and I want to help the club push for their targets."