The 26-year-old has made just 27 appearances for the Terriers since joining in 2011 and has linked up the promotion-chasing Gills in search of first-team football.
Robinson signed for Huddersfield from Bournemouth, where he made 117 appearances and scored 10 goals. Prior to that he played for non-league side Weymouth for two years.
Boss Martin Allen told the club's official website: "I have watched Anton for a long time through non-league football and seen him develop into a strong, athletic central midfield player.
"I drove up to meet him and his wife and they are both very happy and excited to be joining our club. He will be training with us over the weekend and go into our squad for Monday night."
Meanwhile, striker Ben Strevens has left the club for Dagenham. The 32-year-old scored two goals in 14 appearances for the Gills after joining in the summer.
Allen added: "Ben Strevens has been a top professional, a good player and is a really good person around our club. However, with the arrival of Cody McDonald and the option of playing Myles Weston up front the opportunities to actually start games have been limited.
"I'm sure he will do very well for Dagenham and we wish him the very best of luck in the future."