The center back flew into England this weekend to finalize the move which will see him rejoin manager Erik ten Hag, who moved to United from Ajax.
The 24-year-old Martínez still has to pass a medical examination and sign a contract.
"Manchester United is delighted to announce the club has reached agreement with Ajax for the transfer of Argentine international defender Lisandro Martínez, subject to medical, to player terms being finalized, and to UK visa requirements,” United said in a statement on Sunday.
Ajax said the transfer fee will be 57.37 million euros ($57.9 million) with a potential further 10 million euros for the Dutch club in conditional add-ons.
The 24-year-old Martínez has played seven times for Argentina.