Maghoma, whose contract at Burton expires on July 1, has put pen to paper on a two-year deal at Hillsborough, ending speculation linking the 25-year-old with a move to Middlesbrough.
Maghoma said: "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.
"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 was named in the League Two team of the year 2012/13 and was voted Burton's players' player of the year.
He started out as a trainee at Tottenham before joining Burton on loan in the summer of 2009 and made the move to the Pirelli Stadium permanent the following summer.
The DR Congo international played a key role for the Brewers last season, scoring 18 goals in 50 appearances, as Burton made the play-offs before losing to Bradford in the semi-finals.