The 32-year-old centre back, formerly of Sheffield United and Derby, was unattached.
Red Devils boss Steve Evans told the club's official website: "We have signed a top-class international defender in Claude Davis.
"When I took up a reference on Thursday morning in relation to Claude with Neil Warnock he told me to lock the lad in a room until he had signed, he rates him that highly."
Davis admitted that he was impressed with Evans' persistence, he said: "Steve Evans was one of those managers who spoke with me in the summer and to be fair to the gaffer he has kept in touch with me.
"This football club is very ambitious and they want to be in the end of season play-offs in League 2. That is also my objective."