Herbert said the aim is to use current performance assessment tools across the entire state government and find ways to "optimize systems, revenue and personnel."
Cox, 42, has been DWS director since 2007 and overseen sweeping, controversial structural changes. The governor said the overhaul saved taxpayers $30 million and helped DWS meet employers' needs.
"I share Governor Herbert's commitment to optimize all state resources for the taxpayer, those seeking services and Utah's future," Cox said. "A principle-driven approach to budgeting and operations will solidify Utah's decisive, competitive edge as the best-managed state in the nation."
Former state Rep. Ron Bigelow will continue in his role as the governor's budget director. DWS Deputy Director Jon Pierpont has been named acting director.
Ally Isom, the governor's spokeswoman, said adding to the Governor's Office of Management and Budget can increase efficiency because Cox will look for in savings across government, as well as in the budget office itself. That doesn't mean layoffs are coming, she said, but cost-saving moves such as purchasing software across departments has been something "agencies wouldn't realize because they're operating in organizational silos."
The Legislature will have to formally create the new office of management and budget during the 2013 session.
Before coming to Utah, Cox, who is blind, was the running mate of Maryland Gov. Robert Ehrlich in 2006, but lost that race.