The versatile star will reunite with Erik ten Hag at Old Trafford, with the deal understood to be worth £46million and the defender will pen a five-year contract.
A United statement read: "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."
Ten Hag knows Martinez well from his tenure at Ajax, with the Argentine one of his key players at the Eredivisie giants before he left for the Red Devils this summer.
And the Dutchman was clearly keen to reunite with the versatile defender, who made 36 starts in all competitions under him last season.
Martinez was left out of Ajax training on Thursday to tie up his move to United, and will join his new teammates on their pre-season tour of Australia.
Premier League rivals Arsenal were also keen on the 24-year-old and had two bids rejected by Ajax, but it is understood Martinez only wanted to go to United.
The Argentina international played a key role in Ajax's back-to-back Eredivisie title wins, where he played in a number of positions, including centre-back, left-back, and centre-midfield.
It remains to be seen where he will play most often in United's first XI.
Standing at 5ft 9in, many have commented on the prospect of him going straight into Ten Hag's back two, especially with a Manchester derby against Man City's new giant striker Erling Haaland to come, with the Norwegian standing at 6ft 5in.
But fans need not worry, as Martinez has already shown the height difference is no disadvantage.
In fact, Martinez is known as a 'butcher' in his native Argentina, and has won more aerial duels than 6ft 3in United captain Harry Maguire.
Martinez and Haaland actually went head-to-head last season as Ajax faced Borussia Dortmund in the Champions League, and Haaland didn't get a sniff as Ajax won 4-0 in their only game against each other.
"Ten Hag obviously rates the players he's going back to Ajax to get, and thinks they're better than what he's got at Manchester United," former Man City star Trevor Sinclair told talkSPORT.
"Martinez is my height, him against Haaland would be like me marking Lukaku with a ball into the box!
"But Ten Hag obviously trusts he has the attributes to deal with it.
"He's a strong player, he's a good athlete, he reads the game well and the fact he plays in midfield too shows you that he's technically very good."
Martinez is Man United's second signing of the Ten Hag era, following the arrival of another player from the Dutch top flight - Tyrell Malacia from Feyenoord.
But the Red Devils are not done yet, with the club still chasing a deal for Barcelona midfielder Frenkie de Jong - who Ten Hag also managed at Ajax.
United chiefs are in Spain in an attempt to get the transfer over the line.