The Argentine centre-back was kept out of Ajax training on Thursday morning ahead of a move to Old Trafford.
It will see the 24-year-old reunite with manager Erik ten Hag following his appointment at the Red Devils.
Martinez was also being tracked by Premier League rivals Arsenal, but it is United who have won the race.
"Manchester United have now agreed a £46m fee with Ajax for Lisandro Martinez," talkSPORT's Alex Crook told White and Jordan.
"He's been kept away from Ajax training this morning, according to sources in the Netherlands, to tie up this move to Old Trafford.
"He will join United this weekend on their pre-season tour of Australia.
"This is a big deal for Erik ten Hag. He was presented with Villarreal defender Pau Torres as a possible centre-back option, but the coach said no.
"He wanted Martinez from the beginning. Arsenal had two bids rejected by Ajax, and the Gunners took a back seat when Martinez made it pretty clear he only wanted to go to United to link up with Ten Hag.
"I think symbolically this is a very big transfer for Manchester United."
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