The Santiago Bernabeu side already announced on Sunday that they have reached an agreement with Tottenham over the transfer of the Welshman, with Bale set to sign a six-year deal with Madrid.
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"The player successfully passed the tests and then went to the Santiago Bernabeu to sign his contract with los Blancos and to be presented at the Royal Box.
"The player arrived at the Sanitas La Moraleja hospital at 08:30BST, where he underwent various tests: blood and urine analysis, electrocardiogram, echo cardiogram, MRI, radiological and biomechanical study and cardio-respiratory examination."
The 24-year-old's official unveiling is scheduled for 12:00BST.