The Bayern board held an emergency meeting at the Allianz Arena to discuss the issue and Hoeness tendered his resignation.
"After intense discussion, the advisory board of FC Bayern Munich AG decided unanimously that Uli Hoeness should continue in his position of president," said the club in a statement.
Hoeness recently made a self-denunciation to the German tax authorities that he had not declared taxes on an account he held in Switzerland.
He is currently being investigated on suspicion of tax evasion and had offered to resign from his position while the investigation took its course.
"Uli Hoeness expressed his regret at the incident and apologised," continued the club statement, stating that the decision to turn down his offer to resign was made "in the interests of FC Bayern, who need to concentrate fully on reaching further sporting goals with the Champions League final on 25 May and the German Cup final on 1 June."