The English giants will pay 57million euros (67m pounds) with 10m euros of add-ons for the 24-year-old Argentine centre-back who has been with Ajax since 2019.
Martinez, who has seven Argentina caps, played under new United boss Erik ten Hag at Ajax.
The club said in a statement: “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.”
The Argentine will follow Tyrell Malacia and Christian Eriksen into Old Trafford as new signings as part of ten Hag’s overhaul.
Edinson Cavani, Jesse Lingard, Juan Mata, Nemanja Matic, Andreas Pereira and Paul Pogba have all departed the club this off-season.
Martinez had on Friday posted an image on Instagram of him and his agent on a plane with the caption “heading to Manchester”.
He was Ajax’s Player of the Year in 2021-22 as they won the Eredivisie and reached the UEFA Champions League last 16.
Gualeguay-born Martinez came through at junior level with Newell's Old Boys, moving to Defensa y Justicia before ten Hag took him to the Netherlands in 2019.
Martinez will compete with club captain Harry Maguire, Victor Lindelof, Eric Bailly and Raphael Varane to be part of the side’s preferred centre-back pairing.