Martinez has signed 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 Argentina international arrived at United's training ground on Tuesday ahead of confirmation of his move.
Martinez said: "It's an honour to join this great football club. 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."
He made 118 appearances for the Dutch champions after joining the club in 2019 and 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.
John Murtough, Manchester United football director, said: "Lisandro is an outstanding player who will bring further quality and experience to Erik [Ten Hag]'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."
Meanwhile, Cristiano Ronaldo arrived at United's training ground on Tuesday to hold talks over his future at the club. The Portugal international made an official request to leave United this summer so he can continue to play Champions League football next season, sources confirmed to ESPN.