Cousins, who was due to step down from the role this year after more than a decade at the company, was killed alongside four members of his family in a plane crash in Australia on 31 December.
The catering group said the 58-year-old's retirement had been planned for 31 March, but it has advanced Blakemore’s appointment following the sudden accident.
“We are deeply shocked and saddened by this terrible news,” said Paul Walsh, Compass Group chairman.
“The thoughts of everyone at Compass are with Richard’s family and friends, and we extend our deepest sympathies to them.
“It has been a great privilege to know Richard personally and to work with him for the last few years. Richard was known and respected for his great humanity and a no-nonsense style that transformed Compass into one of Britain’s leading companies.”
Cousins joined Compass in 2006 at a time when the company was under fire from Jamie Oliver for serving Turkey Twizzlers in schools.
He was widely credited with turning the business around, and the group reported a 15% rise in annual revenues to £22.6bn in the year to 30 September 2017.