Midfielder Collison has been out of favour under Hammers boss Sam Allardyce this season.
He has made just three appearances and two of those were in the Capital One Cup. He came off the bench against Stoke last month for his only Premier League action.
The Wales international will now spend a month on loan on the Dorset coast.
Bournemouth boss Eddie Howe needs midfield cover with Richard Hughes suspended and Harry Arter and Shaun MacDonald both injured.