The orders were issued late today by the ministry, official sources said.
The board, also the administrative authority of the Income Tax department, is the apex body for collection of direct taxes in the country.
Sharma, a 1976-batch Indian Revenue Service officer, has been given the charge after incumbent Poonam Kishore Saxena retired today.
She was till now serving as a member (Legislation and Computerisation) in the seven-member CBDT, which includes the Chairperson.
The officer has served as Director General (Vigilance) of the I-T department in national capital before her appointment to the top body.