Public prosecutors said in a statement that they did not plan to contest the three-and-a-half-year prison term handed down last week to Hoeness, 62.
Hoeness was sentenced on Thursday for cheating the state out of 28.5 million euros ($39.5 million) after a four-day trial that riveted football-obsessed Germany.
He admitted hiding his wealth in secret Swiss bank accounts while obsessively "gambling" on stock and currency markets for years before seeking to come clean in return for immunity from prosecution.
After the verdict was handed down, he walked out of the courtroom in the southern city of Munich pending an initially-planned appeal.
But a day later Hoeness announced he would forego appealing the sentence, resigning from his posts as president and board chairman of the champion club where he spent four decades.
The prosecution, which had called for a longer jail term, had also been considering an appeal.
"The Munich II public prosecutor's office will, in the criminal proceedings against Ulrich Hoeness over tax fraud, not file an appeal against the verdict," its statement said.
No date has been set yet for Hoeness to begin his jail term, but it is expected to start in the next few weeks.