The Wales international has made just one Premier League appearance for the Hammers this season and two in the Capital One Cup.
His arrival helps boost a squad with plenty of midfield absentees. Collison's fellow countryman Shaun MacDonald is suffering with a knee problem, Richard Hughes is suspended and Harry Arter is also sidelined.
Since making his debut in a 2-0 defeat at Arsenal in 2008, Collison has made 104 appearances and scored 13 goals.
He is available to make his Cherries debut in Tuesday night's Championship trip to Leeds.
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