The London-listed firm earlier this year said Walsh would not seek re-election at its annual general meeting and that it was looking for candidates to take over from the businessman who has been Compass' chairman for nearly seven years.
Meakins' faces a rough road ahead at Compass, as the pandemic forced the world's biggest catering group to raise 2 billion pounds ($2.6 billion) in capital in May to ride out the coronavirus crisis following a profit warning in March.
"I look forward to working with ... the executive team to drive forward the Group's strategy and ensuring that it continues to create significant value for all stakeholders," he said in a statement.
Meakins is currently the chairman at energy services provider Rexel and has also served in various capacities at Travelex, Alliance Unichem and Centrica.
Compass, which employs about 600,000 people globally, serves daily meals to hundreds of thousands of school kids, office workers, armed forces and prisoners.
(Reporting by Pushkala Aripaka in Bengaluru; Editing by Aditya Soni and Amy Caren Daniel)