Bates had recently said he wanted to add experience to his side and the arrival of the 28 year-old does just that, writes Tom Feaheny.
Anderson started his career at Leyton Orient, before having spells at Aberdeen and Blackburn Rovers.
He would then spend three years in Italy, with five different sides.
In 2016 he returned to England and joined Barrow, he made 23 appearances for Torquay.
Before moving to Chester initially on loan before the move was made a permanent one.
"I am looking forward to the challenge, I am very happy to be here, I will aim to give my all," Anderson told the club's website.