The 25-year-old was released by the League One side last month and Allen has wasted little time snapping him up.
Gregory has penned an 18-month deal at Priestfield and becomes the Kent club's second capture of the January transfer window after defender Leon Legge.
Gregory started his career with Wycombe before dipping into non-league football and later returning with AFC Wimbledon, helping the Dons earn Football League status.
The Cherries secured his services in the summer of 2011, but he found his first-team opportunities limited at Dean Court this season and spent three months back on loan at Kingsmeadow.
