Soro was in Madrid early in the morning to pass his mandatory medical examination and sign his contract with Real Madrid.
Real Zaragoza will receive €2.5m up front, plus a similar amount in bonuses.
Soro will sign a deal for five years with Real Madrid, although he will remain on loan this season in La Romareda.
It was Soro's decision to remain with Zaragoza, rather than join Raul's Castilla team this season.
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