His sons Emiliano, who was a player, and Michael, a member of the backroom staff, have also left the club.
Chairman Firoz Kassam said: "Ramon Diaz has ended his time as manager of Oxford and left both the club and the country.
"Ramon's decision lo leave was unexpected and came at a time when negotiations were still ongoing. I am disappointed we were not able to reach an agreement.
"I am disappointed that we were not able to reach agreement, but believe the substantial financial package involved of close to a million pounds would not have been in the interests of the club."