"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," he wrote in a statement published on the club's website.
"Tax evasion was the biggest mistake of my life," he said.
Judge Rupert Heindl ruled on Thursday that Hoeness's voluntary disclosure of tax evasion was incomplete and therefore did not meet a vital requirement for amnesty laws designed to encourage tax dodgers to come clean.
Hoeness, 62, had admitted evading taxes on income earned in secret Swiss bank accounts, but had hoped for leniency in one of the most closely watched tax evasion cases in German history.
The case hinged on the question of whether Hoeness, who as a player helped West Germany win the 1974 World Cup, cooperated fully with his voluntary disclosure. His case shocked the nation and prompted thousands of tax dodgers to turn themselves in.
Hoeness was first charged with evading 3.5 million euros in taxes. But when the trial began on Monday he stunned the court by admitting he had actually evaded five times that amount - or 18.5 million euros.
That figure was raised further to 27.2 million euros on the second day of the trial based on testimony by a tax inspector. Hoeness's defence team acknowledged the higher figure.
Hoeness said he would step down from his positions with the club in order to spare Bayern Munich, a team which last year won the Champions League and which dominates the German Bundesliga, any damage.
The club's earnings have soared under his stewardship, which has lasted 35 years in various posts. With more than 220,000 members, it is one of the world's biggest soccer clubs.
"Bayern Munich is my life's work and will also remain so," said Hoeness, who had been a friend of Chancellor Angela Merkel and a popular TV talk show guest. Ironically, he had spoken out for higher taxes and railed against tax evasion.
FC Bayern Munich AG is privately owned. Major German companies Adidas AG ADSGn.DE, Allianz ALVG.DE and Audi AG VOWG_p.DE, all of which are based in Bavaria, each have an 8.3 percent stake in the club. Deutsche Telekom AG DTEGn.DE is the club's main advertising sponsor.
Members of the supervisory board include Adidas chief executive Herbert Hainer, Audi CEO Rupert Stadler, Volkswagen CEO Martin Winterkorn and Deutsche Telekom CEO Tim Hoettges. (Reporting by Alexandra Hudson; Editing by Stephen Brown)