An emotional Calderon announced his decision at a press conference after tendering his resignation to the board of directors in a midday meeting.
Vice-president Vicente Boluda will take charge until the elections, which have been brought forward to this summer.
Calderon, who was moved to tears at the press conference, revealed he felt his position had become untenable following allegations of voting irregularities at the club’s last general assembly.
“Against the opinion of every one of my board members, I have decided to hand the presidency of the club to Vicente Boluda,” he said.
“I deliver up my head, which has been persecuted so much since my arrival, because I hope it will help pacify a social mob who are permanently upset and in fits by news that the press spreads, which is exaggerated with complete disregard to moral codes.
“I walk away with clean hands and a clear conscience, and less money and health than when I started.”
He added: “I have nothing to hide and firmly deny all the lies that have been published by various media sources in the past few days.
“I never participated in anything illegal or committed any wrongdoing.
“The success of those who looked for my destruction is also the triumph of injustice and wickedness.
“I may have committed mistakes but never irregularities.”
Calderon took charge of Madrid in July 2006 and oversaw back-to-back titles at the Spanish giants.
The club have had a troubled start to this season, which saw the dismissal of coach Bernd Schuster last month.
However, Calderon insists he is satisfied with his time at the helm.
“I leave with my head held very high and a very calm conscience,” he said. “I am extremely proud to have served the best club in the world. I can say that my time here has been a success in which we have seen many triumphs.
“I feel for this club and want what’s good for it with all my heart and I have a lot of pride in the players, staff and those in the junior ranks.
“I thank them all for their support and hope everyone continues to show respect towards them. They can win all the competitions they’re fighting for.
“I will always support anyone who succeeds me at the club and never react against them or oppose them.”
The new interim president also said a few words at the end of the press conference, where he pledged to give his all during his brief spell in charge.
“I will dedicate myself completely to the club,” said Boluda. “And I will ask all staff to do the same, to show unity and responsibility.
“I ask them also to allow me to rule the club in a calm and confident atmosphere. Our teams can win all the competitions they are involved in and they deserve to have us by their side.”