In a statement announcing his resignation, Azharuddin Abdul Rahman said although the report released on Monday did not blame his department for the plane's disappearance, it found that air traffic controllers had failed to comply with standard operating procedures.
The jet carrying 239 people from Kuala Lumpur to Beijing vanished on March 8 2014 and is presumed to have crashed in the far southern Indian Ocean.
Commenting on his resignation, Mr Rahman said in a statement that it was "with regret and after much thought and contemplation" that he would resign - four years after the disaster.
The Malaysian civil aviation authority's chief resigned on Tuesday, a day after an independent report on the disappearance of the Malaysia Airlines flight MH370 found lapses by air traffic controllers working at the control center in Kuala Lumpur.
A slow response by air traffic controllers in Malaysia and Vietnam delayed the launch of search and rescue operations, it said, while the battery in the plane's emergency locator beacon had expired.
The disappearance of the Boeing 777-200 triggered the largest hunt in aviation history.
Kok also said that the 449-page report was not a final report on the search for the missing aircraft but was only on the safety investigation and it was separate from search and judicial investigations.
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The safety team, comprising accredited representatives from eight countries including the USA, the UK, China, Australia, France, Singapore and Indonesia, released a 1,500page investigative report based on evidence gathered and data analysed over the period of four years.
The report said there was insufficient information to determine if the aircraft broke up in the air or during impact with the ocean.
Although the underwater search turned up nothing, small pieces of debris from the plane were washed up on islands in the Indian Ocean and on the African coast.
Malaysia's government has said it will resume searching if credible evidence of the plane's location emerges. Extensive sonar searches of remote waters off Australia's west coast failed to locate the wreckage.
United States exploration firm Ocean Infinity resumed the search in a different location at the start of this year on a "no find, no fee" basis, using high-tech drones to scour the seabed.
New Malaysian Transport Minister Anthony Loke said the government will investigate and take action against any misconduct based on the report findings.
Meanwhile, Intan Mazurka Othman, whose husband was a steward on the jet, said she is frustrated that there is "nothing new in the report".