The clubs have agreed a fee of €35m with €10m worth of potential add-ons with Lindelof's club, Benfica.
"Manchester United is pleased to announce that it has reached agreement with Benfica for the transfer of Victor Lindelof, subject to a medical examination, international clearance and personal terms," read the statement on the club website.
The Sweden centre-back made 47 appearances for Benfica last season.
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