The 23-year-old has spent the previous two campaigns on loan at Elland Road making 91 appearances and scoring 10 goals in all competitions and Leeds said they completed his loan deal with a view to signing him permanently.
He is Leeds' third recruit of the transfer window following the permanent arrivals of on-loan signings Helder Costa and Illan Meslier this month.
A former youth player with Manchester United and Liverpool, Harrison has also represented England at under-21 level.
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He played all 46 league games for Marcelo Bielsa's side last season, as they ended a 16-year wait to return to the English top-flight by winning the second-tier Championship.
Leeds have also signed 18-year-old Joe Gelhardt on a four-year deal from Wigan.
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