Ajax confirmed United will pay an initial 57 million euros ($57 million, £48 million) with a further 10 million euros in performance-related bonuses.
“Manchester United is delighted to announce the club has reached agreement with Ajax for the transfer of Argentine international defender Lisandro Martinez, subject to medical, to player terms being finalised, and to UK visa requirements,” United said in a statement.
Martinez is set to be reunited with his former boss Erik ten Hag at Old Trafford.
Ten Hag has already added midfielder Christian Eriksen and left-back Tyrell Malacia to a squad that finished a disappointing sixth in the Premier League last year.
Martinez moved to Ajax from Defensa y Justicia in his homeland, winning two Eredivisie titles and helping the Dutch champions reach the last 16 of the Champions League last season.