Mr Mehrishi, 62, would be administered the oath of office and secrecy by President Ram Nath Kovind at Rashtrapati Bhavan tomorrow, they said.
His appointment has been cleared by the government, the officials said.
Mr Mehrishi, a 1978 batch (retired) Indian Administrative Service (IAS) officer of the Rajasthan cadre, completed his two-year fixed term as the home secretary last month.
Mr Sharma, who had taken over as the CAG on May 23, 2013, demitted office on Friday, they said. Mr Sharma was defence secretary prior to his appointment as the CAG.
Mr Mehrishi will have a tenure of about three years.
The CAG is appointed for a term of six years or till the incumbent attains the age of 65 years, whichever is earlier.
As a constitutional functionary, the CAG is primarily entrusted with the responsibility to audit the accounts of the Union government and of the state governments.
Mr Mehrishi, who hails from Rajasthan, holds Master of Business Administration degree from the University of Strathclyde, Glasgow (UK).
He also possess Master of Arts (MA) and Bachelor of Arts (BA) degrees from Delhi University.
Mr Mehrishi has held several posts in both his state cadre Rajasthan and in the Centre.
Before appointed as the home secretary, he worked as economic affairs secretary and chief secretary of Rajasthan.
Mr Mehrishi has also worked as secretary in departments of chemicals and fertilisers, and Overseas Indian Affairs.