The 56-year-old was on Friday sentenced to seven years in jail at Madrid's Supreme Court after being found guilty of involvement in the mis-use of public funds in the southern resort town of Marbella.
His resignation from Sevilla's board followed on Monday morning, with the club's official website reporting that he was given a "loud roar of applause" as he prepared to end a reign of 11 years, six months and nine days.
"I apologise to Sevilla," he said.
"We have reached a day we never expected, the least desirable and I have a battered heart.
"In my 27 years of involvement with Sevilla I have been available for this club and all it has needed off me.
"Today I leave with regret, with a deep sadness and with humility."