Kennedy, commonly known by his initials RFK Jr, has a history of spreading health information that scientists say is false. If his nomination is approved by the Senate, he will lead a huge agency overseeing everything from food safety to medical research and welfare programmes.
Trump told supporters at his election night victory party that Kennedy wanted to "help make America healthy again".
RFK Jr suffers from spasmodic dysphonia. For information on this, please click here.