Barry has put pen to paper on a four-year contract at Hillsborough, with the club holding an option for a further year.
He built his reputation during three loan spells at Stockport County, where he scored 29 goals and added seven assists in 56 appearances, and also has Championship experience from a spell at Hull City, having first come through the ranks at Barcelona before returning to England with Villa in 2020.
"I'm buzzing and I can't wait to get started - it's just about finding a home and this is the place I want to be for the next part of my career," Barry said.
"It's now time to settle down and find a home and I think that will come out in my performances as well. I've walked into a really warm atmosphere. Getting a good pre-season under my belt is a massive thing to build connections and to get used to the style of play straight away.
"I feel like I can progress at the same speed as the club wants to, which is fantastic. To call a club your own is just a great feeling."
Sporting director Simon Wilson, who worked with Barry during his time at Stockport, said the move had long been the player's preference.
"Louie's determination to make this move happen has been relentless," Wilson said. "He had multiple options available this summer, including opportunities in the Championship, but he was clear from the outset that he wanted a permanent home - and for him, it was only Sheffield Wednesday. Henrik, Louie and I all believe in the synergy of this move - the right player joining the right club at the right time.
"He brings goals, directness and real attacking quality, with attributes that are closely aligned to the playing identity we are building. He has already shown what he can do at this level, but there is much more to come. With the stability of a permanent home, our coaching environment and the backing of our supporters, we believe Louie can become an important player for Sheffield Wednesday for many years to come."