The Republic of Ireland U19 international has been with Villa since 2018.
"I'm absolutely delighted to be here," Wright said after his move was confirmed. "I just want to thank the gaffer and Walsall for giving me the opportunity to come here on loan. I have been waiting a long time for this opportunity and I just can't wait to get started.
"It means a lot to me (to be allowed out on loan) to be fair. I want to go out there and showcase my ability and show everyone what I have got.
"Like I say, I have been waiting for this opportunity for a long time. Playing men's football will be a huge development in my career and hopefully it is a step towards great things.
"I'll take my experiences of playing in the EFL Trophy this season because I haven't played men's football before but those games are a massive help and they can really help with your career development and I have enjoyed playing in those games."