The Cherries have also been boosted by news Rhoys Wiggins has extended his temporary deal from Crystal Palace until the end of the season.
Manager Eddie Howe told the Bournemouth Daily Echo: "I always maintained I would only sign players I felt would improve the squad and Anton and Liam will certainly do that.
"Both permanent signings are the right age and will give us mobility, speed and energy, qualities which are so important in the modern game.
"Rhoys has come in and performed really well. Prior to signing, he had played little football for eight weeks but you wouldn't have known that from his performances."