Pelham, who has held senior civil service positions at the Cabinet Office, Home Office and the former Department for Constitutional Affairs, will replace Eric Prescott, who quit with immediate effect in May after 18 months in charge.
A spokeswoman for the organisation refused to reveal how much Pelham would be paid, saying the information was confidential. Her salary at the JAC was between £115,000 and £120,000 in 2009/10, its annual accounts show.
Ilyas Khan, chair of Leonard Cheshire, said in a statement: "Clare’s experience of managing complex organisations and running large national projects has equipped her to lead our charity, but it is her deep personal commitment to disabled people and the achievement of their rights that qualify her for the job."
The statement did not say what the nature of the personal commitment was and the spokeswoman was unable to provide details.
Pelham, who has also worked for IBM and Coca-Cola GB & Ireland, said in a statement that she had worked as a volunteer for the charity when she was a student and was "profoundly impressed" by the people she had worked with.
"The charity is dedicated to supporting and encouraging disabled people who seek greater control over their own lives and more than anything else I hope to play a part in doing this," she said.
Pelham’s start date has not been finalised, but she is expected to join the organisation towards the end of 2010.