Charles has been at Sixfields for almost a year after joining the Cobblers from Aldershot at the end of the last January transfer window.
After 20 appearances, the 31-year-old is now free to join another club.
"I think it is right to be honest with people," Northampton boss Boothroyd told the club's official website.
"While Anthony has never let us down, being honest with him, he was going to find first-team opportunities limited moving forward and he was not going to be offered a new contract here in the summer.
"With that in mind, it was felt best that he moved on and he will hopefully get to play more regularly elsewhere. We wish Anthony well.
"I also feel we are top-heavy on defenders and we need to look to strengthen further up the pitch."