Her appointment follows the departure of current Royal Parks chief executive Mark Camley who is to take over as director of park operations for the London Legacy Development Corporation on 3 January.
Prior to joining the Parole Board Lennon was area director for the Civil and Family Courts in London and worked for 30 years in the courts of London and the South East.
Lennon said: "I am really looking forward to taking on this exciting and challenging role and working with the board, staff and stakeholders to deliver a successful 2012 and a sustainable long-term future for the parks," said Linda.
Welcoming the appointment the chairman of the Royal Parks Board Apurv Bagri said:
"I am delighted that Linda will be joining the Royal Parks early in the New Year. Her experience and proven track record will be really important to us in what promises to be an exciting year for the parks with the Diamond Jubilee and the Olympic and Paralympic Games."