Stuttgart-based Porsche said in a statement that an agreement on the resignations had been reached with the supervisory board and that Wiedeking - said to be the best-paid boss in Germany - would get a golden parachute worth €50 million, of which half was to go to a "social foundation."
Porsche's current production chief Michael Macht, 48, is to succeed Wiedeking, who together with Härter was the architect of Porsche's bid to take over Volkswagen (VW), Europe's biggest automaker.
Porsche currently owns nearly 51 percent of the shares in VW, with which it has been in conflict for several months.
The statement said Wiedeking and Härter considered the step "a significant contribution to the appeasement of the situation and to support the forming of an integrated car manufacturing company" with Volkswagen.
A power struggle between Wiedeking and the head of VW's supervisory board, Ferdinand Piech, had tarnished both companies, and was said to be blocking an investment deal with the Gulf state of Qatar.
Late Wednesday, the Porsche supervisory board approved Wiedeking's plans for a capital increase of at least €5 billion, and talks with Qatar over an additional capital injection.
The measures should allow Porsche to pay off at least part of its estimated €10 billion in debt.
But Porsche, which is owned by the Porsche and Piech families, finally decided to jettison Wiedeking and Härter, saying that the two directors had also "come to the conclusion that the further strategic development of Porsche... is better off, if they are not on board as acting persons."
In a separate statement, Wiedeking said he would give a large part of his severance package to charities, saying the decision was based on "personal reasons and (my) responsibility to society."
He planned to create a foundation to aid in the development of "socially just" production sites for Porsche in cooperation with the company's works council.
Around €1.5 million was also to be donated to foundations that help journalists in need.