24-year-old Rose is a product of West Bromwich Albion's youth system where he progressed through the various ranks to pen pro terms in 2014.
Following loan spells with Accrington Stanley and Crawley Town Solihull-born Jack was released by the Baggies in the summer of 2017 before joining Southampton later that same summer.
Rose will provide competition for current Saddlers number 1 Liam Roberts as he looks to earn some much-needed first-team football in the Black Country.
Speaking to iFollow Walsall, Jack said; "I am over the moon to be with Walsall for the season. It’s a local team for me, I am excited to be here and I am excited to be around a first team environment and I can’t wait to get going.
"I have spoken to most of the lads this morning and they seem like a great bunch to be honest with you. Everyone has been very welcoming and to come in so early into pre-season, it is great for any player because you are able to get a feel of the place and nothing is awkward for you then.
"I am very excited to work under Maik Taylor, I used to watch him as a young lad when he was playing. I know he has got a wealth of experience and I am just looking forward to being able to pick his brain at every possible opportunity."