The team said Cregan has decided to "move on and take an exciting new role elsewhere within motorsport" and that his new position would be confirmed in due time.
Forty-eight year-old Cregan had joined Toyota 24 years ago as a rally mechanic.
Jens Marquardt, who has been at Toyota Motorsport since 2000 working in the engine engineering department, will replace Cregan.
"We are very sad to be losing a team member of Richard's qualities but we understand his reasons and we wish him the very best of luck in his new challenge," said Toyota's team principal Tadashi Yamashina. "Richard played an important part in Toyota Motorsport's history.
"We salute his numerous achievements, which include providing a positive working environment at the factory and at tracks around the world as well as implementing the Toyota Way in Formula One, where we have achieved significant progress in areas such as pit stops and car operations.
"Looking to the future I am delighted Jens will take this new opportunity, which he thoroughly deserves. Jens has been with our company for eight years and is a valuable team member who has shown great ability and a positive attitude. He has a suitable amount of time to learn his new tasks from Richard and we are confident the transition will be a smooth one."
AUTOSPORT
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