Having spent a short time training with the squad earlier in the campaign, the midfielder has agreed a two-year contract.
"Sean is a player I’ve been interested in for a while now, and I’m delighted to bring him in to strengthen our midfield options," ’Well manager Graham Alexander said of his signing.
"I believe he has great untapped potential to be a top player with the ability he has, while we can help him improve the things he needs to.
"He also has previous experience of Scottish football and we look forward to working with him.”
Goss, 25, started his professional career at Old Trafford, where he was a team-mate of current 'Well favourite Liam Grimshaw.
Sold to Queen's Park Rangers for £500,000 in 2017, he subsequently spent time on loan in Scottish football with Rangers and St Johnstone, before a switch to Shrewsbury Town in 2019.
It was there he made 54 appearances across two seasons in League One, scoring four times, before his contract expired in the summer.
Goss is of Northern Irish descent through his grandparents, and in 2018 then manager Michael O'Neill, sought to call him up to the Green Army squad.
He joined Juhani Ojala, Callum Slattery, Darragh O'Connor, Liam Kelly, Connor Shields, Kaiyne Woolery, Justin Amaluzor, Kevin van Veen and Mich'el Parker in signing for ’Well this summer.