Replacing Richard Peel, who left in January to set up consultancy RPPR (PRWeek, 6 January), Grey will arrive after three years at the patient safety body.
The Audit Commission - which monitors local government services with a focus on housing, health, and fire and rescue - faces radical reform this year. The Government has proposed distilling the country's 12 watchdogs into just five organisations.
The commission faces taking on extra responsibilities as part of the reform.
'There will be fewer regulators in the public sector after this year,' said Grey. 'Our challenge will be to engage people and communicate the concept of value for money. Generally people do not know they can access information about local services [from the commission].'
Meanwhile, the commission has been challenged by the Government to rate local services by recorded customer satisfaction, rather than via external audits.
Local Government Association director of strategy Oona Muirhead said the public sector is increasingly adopting user satisfaction as a measure of its services - meaning the role of bodies such as the Audit Commission is likely to be reduced.
Grey will report to CEO Steve Bundred and will sit on the management team.
Geronimo Communications board director Marina Pirotta is acting in the post until Grey's arrival.