The 34-year-old has signed a one-year contract and arrives in west London after scoring seven goals and providing one assist in 35 appearances for the Hammers last season.
Wilson began his career at hometown club Coventry City, making his senior debut at the age of 17 before enjoying a prolific breakthrough campaign in 2013/14, when he scored 22 goals and earned a place in the League One PFA Team of the Year.
He later joined Bournemouth, where he played a key role in the club’s promotion to the Premier League in 2015.
“Callum is someone that everyone will be familiar with; he has been a Premier League goalscorer for such a long time,” manager Keith Andrews told club website.
“He gives us more options in that area of the pitch, and will help Igor Thiago and Kaye Furo with the experience that he has.
“He’s just got that nous to score goals, as well as that experience around the training ground.
“This is another really good signing for us.”