Martinez will sign a five-year contract at Old Trafford to reunite with former manager Erik ten Hag in a deal worth an initial €57.37 million, which could rise to €67.37m through variables. The move is subject to a medical.
A statement from United said: "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."
ESPN previously reported the 24-year-old was keen on a move to the Premier League with United his favoured destination. Sources told ESPN that a breakthrough had been made and that Martinez rejected interest from Arsenal.
Martinez can play in defence and in midfield, which are both areas of the squad that Ten Hag is keen to strengthen. Martinez made 118 appearances for the Dutch champions after joining the club in 2019. He becomes Ten Hag's third signing of the summer after Tyrell Malacia joined from Feyenoord and Christian Eriksen moved to Old Trafford after spending the second half of last season at Brentford.
After wrapping up a move for Martinez, United will continue their attempts to sign Frenkie de Jong from Barcelona, but sources told ESPN that De Jong still needs to be convinced to move.
United remain sure the Netherlands international is open to joining the club, but according to sources, his representatives are still trying to encourage Paris Saint-Germain and Chelsea to join the bidding.
De Jong would rather join a Champions League club if he has to leave Barcelona, although his preference is to remain at Camp Nou despite the LaLiga side's insistence he has to move to help the club solve their financial issues. There is also an issue of wages that total more than €20m that Barcelona owe De Jong.
ESPN's Rob Dawson contributed to this report.