The 25-year-old winger joined Burton Albion in 2009 after coming through the academy ranks at Tottenham.
Maghoma helped Burton reach the League Two play-offs last season, scoring 18 goals.
"This is a massive move for me and having walked into the stadium, I can't wait to get started," said Maghoma.
"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 am 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 am very confident I will do that at Sheffield Wednesday."
Maghoma, who was linked with numerous clubs, will join Dave Jones' side on July 1 after his contract with the Brewers expires.