The 24-year-old, who won two Eredivisie titles under United boss Erik ten Hag in Amsterdam, has signed a contract until 2027 at Old Trafford, with the option of a further 12 months.
According to Ajax, the Premier League club have paid an initial transfer fee of 57.37million euros (£48.3m), which could rise by a further 10m euros to around £56.7m.
“It’s an honour to join this great football club,” the centre-back told United’s website. “I’ve worked so hard to get to this moment and, now that I’m here, I’m going to push myself even further.
“I’ve been lucky enough to be part of successful teams in my career and that’s what I want to continue at Manchester United. There will be a lot of work to get to that moment, but I firmly believe that, under this manager and coaches, and together with my new team-mates, we can do it.
“I want to thank Ajax and their fans for all the support they gave me. I had an unbelievable time there but feel the moment is right to test myself in another environment. Now I am at the perfect club to do this.”
Martinez, who began his career at Newell’s Old Boys and also played for Argentinian side Defensa y Justicia, won the 2021 Copa America with his country and has been capped seven times at international level.
He becomes the third signing of the Ten Hag era following the capture of left-back Tyrell Malacia from Feyenoord and the free transfer arrival of former Brentford and Tottenham midfielder Christian Eriksen.
Martinez was named Ajax player of the year for the 2021-22 campaign and made 120 appearances during his three seasons at Johan Cruyff Arena, scoring six goals.
Manchester United football director John Murtough said: “Lisandro is an outstanding player who will bring further quality and experience to Erik’s squad.
“We are delighted that he has chosen to join Manchester United and we are looking forward to seeing him develop further and help the team achieve the success we are aiming for.”