The 19-year-old academy graduate was given his league debut under new head coach Brian Dutton and has since cemented his place in the team.
He has received plaudits from supporters for his impressive displays in recent weeks and now has been rewarded with fresh terms.
Perry is the second player of the day to earn a new deal after Emmanuel Osadebe. The club has not disclosed the length of the contract for either player.
“I am delighted to get the deal over the line and to sign a new contract with the club, it feels great,” he said.
“I feel like I am doing well, I am starting games back-to-back and I can’t thank the gaffer enough for putting his trust in me and for him to keep putting his trust in me for when he does put me in the starting line-up.
“I have to give my all every time that I play and I always will give my all for every game that I play for the rest of this season and moving forward.
“Alfie (Bates) and Kins (Liam Kinsella) have both come through the academy and have both made so many appearances for the first team and hopefully now I can push on and do the same."
Dutton has been a huge fan of Perry since bringing him into the team and has faith in his ability moving forward.
“Sam Perry is the future of Walsall Football Club,” Dutton said.
“He’s an outstanding talent and someone who has got a lot of development left in him but to come into the EFL and show the maturity that he’s already shown has been incredible.
“I’m delighted he has agreed a new deal.”