The 23-year-old has put pen to paper on a three-year deal after leaving Everton as a free agent at the end of last season, becoming the League One club's 13th summer signing following their relegation and takeover by US consortium Arise Capital Partners.
Sporting director Simon Wilson already knows the versatile midfielder well, having signed him on loan twice at Stockport County, and explained why the free transfer represented good business for a club still operating under recruitment restrictions.
"In our circumstances, we have to look for value and as a 23-year-old player with an elite background, a unique physical profile, and that can play multiple positions, Tyler represents a good opportunity for the football club," Wilson said.
"He is like Louie Barry in some senses - very good players at Premier League teams can suffer by going on multiple loans and never having that feeling they belong somewhere and can call it home.
"The long-term deal offers Tyler this possibility and now gives us both time to get our heads down and make it a success."
Onyango, who can operate in central midfield, at right-back or in central defence, spent six years at Everton and made five first-team appearances for the club, including four in the Premier League, having made his debut against Wednesday themselves in the FA Cup back in January 2021. He spent time on loan in League One with Burton Albion, Forest Green Rovers and Stockport County across the last three campaigns.
The midfielder said he was relishing the fresh start at Hillsborough.
"I'm absolutely delighted. What a club and a great opportunity for me. I can't wait to get going. It's been a great first few days and I'm really happy. I know the project and the direction the club is going. I've seen what's happened over the last few years and for me it feels like a new chapter. This is a club moving in the right direction and that's something any player would be excited to be part of.
"As a young player, to join a club that has big ambition is massive. I know a couple of the lads already but the rest of the group have taken to me really well. It's a really welcoming club and somewhere I want to stay and be a part of."