Martin Winterkorn said he was “shocked” by recent events and that Volkswagen needed a “fresh start”.
He added that he was “not not aware of any wrong doing on my part” but was acting in the interest of the company.
VW has already said that it is setting aside €6.5 billion to cover the costs of the scandal.
The world’s biggest carmaker admitted last week that it deceived US regulators in exhaust emissions tests by installing a device to give more positive results.
VW said later that it affected 11 million vehicles worldwide.
“I am clearing the way for a fresh start with my resignation,” Martin Winterkorn said in his statement.
He said he was “stunned” at the scale of the misconduct in the group but that he was confident that VW would overcome this “grave crisis”.
“The process of clarification and transparency must continue. This is the only way to win back trust,” he continued.
In a separate statement, VW’s supervisory board said they would announce Martin Winterkorn’s successor at a board meeting on September 25, adding that it was “expecting further personnel consequences in the next days” as a result of its own investigations.
“The internal group investigations are continuing at a high tempo,” it said.
“All participants in these proceedings that has resulted in unmeasurable harm for Volkswagen will be subject to the full consequences.”
The board also said that it would voluntarily submit a complaint to the state prosecutors.
“In the view of the Executive Committee criminal proceedings may be relevant due to the irregularities,” its statement said.
German public prosecutors have already said they are considering an investigation, with US authorities also said to be planning criminal investigations.
In addition, VW faces fines of up to $18 billion by the regulator, the Environmental Protection Agency (EPA).
VW’s shares have tumbled some 30% since the beginning of the week in response to the scandal.
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