"In the interest of the company he will resign" on Monday, Deutsche Post said in a brief statement posted on the company's Web site. "The executive committee respects this decision and proposes to the supervisory board to accept."
A spokesman for Germany's finance ministry, which first revealed Zumwinkel would leave, was asked whether he believed the allegations against Zumwinkel were accurate.
"We have the impression that Mr Zumwinkel thinks that," Torsten Albig said, adding that anyone who thought they could be implicated in the probe should consider turning themselves in.
The spokesman also told a news conference he expected Zumwinkel would quit as chairman of Deutsche Telekom. Deutsche Telekom had no immediate comment.
German Chancellor Angela Merkel said his departure from Post was unavoidable, while Finance Minister Peer Steinbrueck said the probe had caused considerable "moral damage". The state is Post's biggest shareholder with a 31 percent stake.
Hundreds more rich and prominent Germans faced a visit from police after prosecutors investigating tax evasion got extensive data on offshore bank accounts in Liechtenstein, a paper said.
It was unclear how prosecutors obtained the documents about accounts at LGT, business daily Handelsblatt said, but it quoted one unnamed investigator saying: "We cracked the entire bank."
LGT spokesman Bernd Junkers in Liechtenstein said the bank controlled by the tiny principality's princely family had taken note of the report but could not comment further.
"Clarifications that concern LGT Treuhand AG based in Vaduz are under way," he said, adding LGT Treuhand is an independent unit of LGT Group responsible for setting up foundations.
Named by Manager Magazin as its 2003 manager of the year, multi-millionaire and former McKinsey partner Zumwinkel transformed Post from a sleepy state monopoly to a global mail, logistics and finance group, taking the helm of Telekom's supervisory board in 2003.
Zumwinkel has sought to reduce the company's dependence on its domestic mail business by expanding its DHL express and logistics divisions and through acquisitions.
But he has struggled to reverse losses at DHL Express's business in the United States, and has signalled he could sell retail bank unit Deutsche Postbank.
He said last year he would decide on his future with Post in mid-2008 as his contract runs out in November.
Logistics and mail head Frank Appel has been lined up as a possible successor, while analysts have said the probe could also strengthen the position of John Allan, who became finance chief last year with the task of restoring investor confidence.
A Deutsche Post spokesman declined to speculate on a successor, but told a news conference: "Certainly ... the owners are not in the situation where they have to look around in a hurry for a suitable external candidate. I don't see that happening."
Also this week, Liechtenstein bank LLB said it had been targeted by a blackmail campaign since 2003 after an employee threatened to reveal account details of German clients.
LLB said the employee was arrested and sentenced in 2004 -- and still remains in prison -- but that an accomplice continued the blackmail campaign. One person was arrested in September and remains in investigative custody in Germany, LLB said.