Del Nido, a 56-year-old lawyer and major shareholder of the La Liga club, took charge in 2002 and presided over Sevilla's most successful period during which they won the UEFA Cup in 2006 and 2007 and the Copa del Rey in 2010.
Under his guidance, they gained a reputation for discovering and developing talent and players who passed through before being snapped up by wealthier rivals include Sergio Ramos, Daniel Alves and Jesus Navas.
Del Nido gave an emotional farewell news conference on Monday during which he apologised to the city of Seville and the club's fans for having been found guilty while serving as president.
"The day I never wanted to see has come," he said.
"If I had known that what happened was going to take place, I would have stepped down much earlier."
Del Nido was initially sentenced in 2011 after an investigation into corruption in the city of Marbella. His appeal was rejected by the Supreme Court.
Jose Castro, a club vice president responsible for security and external relations, will take over on an interim basis until a shareholders meeting on Dec. 17, the club announced.
Del Nido said one of his final acts before resigning was to agree a new television deal with broadcaster Mediapro for the years 2014 to 2016. He gave no financial details.
Coached by Unai Emery, the club are currently eighth in La Liga and are through to the knockout stages of the Europa League, Europe's second-tier club competition.