The journalist and author, who will take over the position at the trust (www.nationaltrust.org.uk) from Sir William Proby in November, was chosen after a formal interview process.
The position involves two or three days' work a week and the appointment is for an initial three-year period.
Dame Fiona Reynolds, director-general of the National Trust, said Jenkins would be a powerful advocate for the organisation. "Simon is a hugely respected public figure with a deep understanding of what we do and a passion to move it forward," she said.
Jenkins, who claims to have visited every National Trust property in England and Wales, said it was a great honour to have been appointed.
"I have always been an admirer of the National Trust and I have been a member all my life, so it is with a sense of awe and excitement that I take up this post," he said.