Hoeness, in a statement published on the club's website, said: "After discussions with my family I have decided to accept the ruling of the Munich court on my tax affairs. This befits my understanding of decency, dignity and personal responsibility. Tax evasion was the biggest mistake of my life."
He added: "Bayern Munich is my life's work and will also remain so," insisting he wanted to spare the club any damage.
"I wish to thank from the heart my personal friends and all followers of Bayern for your support," he continued. "I will continue to be associated with this magnificent club and its people in other ways for as long as I live."
Hoeness, 62, who won the World Cup with West Germany in 1974, last year admitted to channelling large profits made on the stock market into a Swiss bank account in a tax fraud calculated to have cost the state more than €28.5m (£23.8m).
The prosecutor Achim von Engel described the case as a "particularly grave case of tax evasion" and called for a sentence of five and a half years in prison.
The state attorney could in theory still appeal to have that sentence imposed, with a decision expected early next week, though that is considered unlikely at the moment. If there is no appeal, Hoeness is likely to begin his sentence in around a week's time.
The defence had originally sought a suspended sentence and has a week to appeal against the verdict though that now appears to have been superseded by Hoeness's statement.
Bayern moved quickly to fill the vacancy left by Hoeness's departure by electing the Adidas chairman Herbert Hainer as his replacement.
Hainer, 59, will assume Hoeness' duties after the club accepted his esignation.
"Uli Hoeness has always served Bayern Munich's best interests with his leadership qualities, his high personal involvement and his exceptional lifetime achievements," Hainer said in a statement.
"He has made a considerable contribution to Bayern Munich becoming one of the most successful and attractive clubs in the world, financially and sportingly, and we will always be extremely grateful to him for this."