The 31-year-old joined the Tigers from Rennes in 2017, making 123 appearances and scoring 25 goals.
Grosicki, who has 73 international caps, joins a West Brom side who sit second in the table for an undisclosed fee.
Baggies technical director Luke Dowling told the club website: “Kamil is one of the most consistent players I have seen.
Signed & sealed. ✍🏼📝
— West Bromwich Albion (@WBA) January 31, 2020
“He’s always a seven out of 10 guy who will give you a nine as well. He’s exactly the type of player we want to be adding at this stage and as soon as he heard of our interest, there was nowhere else he wanted to come.
“He’s got great experience and is still an important member of his national squad with the Euros ahead in the summer.”