Mantom, 20, has impressed during his second loan spell at the League One club and has now put pen to paper on an 18-month deal.
"I am really pleased that we were able to complete this deal," said Saddlers manager Dean Smith. "Sam is a great acquisition for us. He's a young player who understands the game.
"We know all about him and what he will bring to us; he has hunger and a great attitude to progress.
"He's enjoyed his loan spells here and was keen to commit himself to our cause."