The 25-year-old, whose Burton Albion deal was due to expire at the start of next month, had been linked with a number of clubs in recent weeks.
"This is a massive move for me and having walked into the stadium, I can't wait to get started. I really enjoyed my four years at Burton, but the time is right for me to move onto the next stage of my career and this is it," he told the club's official website.
"I'm a very ambitious player, I always work hard on my game from the left and from the right and I always want to improve. I'm very confident I will do that at Sheffield Wednesday."
Maghoma began his youth career at Tottenham Hotspur.