Pettigrew will become a non-executive director from 1 January 2018, and will also be a member of the audit and nomination committees.
Pettigrew was appointed chief executive of National Grid last year, and has worked at the company for over 25 years.
"We are delighted to welcome John to the Board of Rentokil Initial," said Rentokil chairman John McAdam.
"His international experience of developing and implementing strategies for profitable growth, and in leading a business with a large field-based workforce, will be very valuable in the Company's continued development."
The appointment comes after non-executive director Chris Geoghegan stepped down from the Rentokil board in September due to his links to the Bell Pottinger scandal.
Rentokil also added Oxford economics professor Dr Linda Yueh to its board earlier this month.
The company has been on something of an M&A spree, acquiring 34 other businesses so far this year, and has said the acquisition pipeline remains strong.