The 26-year-old, who joins for an undisclosed fee, moved to Valley Parade last summer and scored four goals in 30 starts for the Bantams this term.
He previously had a two-year spell at Oldham, but has agreed a contract until the summer of 2010 with the Owls.
However, he will be suspended for his first two Wednesday matches.
"We have gone for him because he's got something not many teams have - electric pace," Brian told www.swfc.co.uk. "He is as quick running with the ball as he is without it and will give us the dimension we need either out wide or up front.
"It also gives us cover at a time where we've been looking to strength in wide area and Jermaine can play both on the right, left and up front.
"I think the supporters will love him because he's one of those players who gets you on the edge of your seat."