According to the BBC, the transfer includes an initial £48m fee plus £2m in achievable add-ons, while Chelsea have secured a 10% sell-on clause.
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Santos has been cleared to undergo his medical, with the move expected to be completed soon.
The Red Devils moved quickly after identifying central midfield as a priority following Casemiro’s departure and Manuel Ugarte’s injury setback.
The club had explored moves for Elliot Anderson and Mateus Fernandes but failed to reach agreements.
Santos will become Chelsea’s latest major summer departure and is expected to strengthen Michael Carrick’s midfield options ahead of the new season.