The Appointments Committee of the Cabinet, headed by Prime Minister Narendra Modi, approved these appointments for an initial period of two years, it said.
Kothari, a 1978-batch IAS officer of Haryana cadre, retired in June last year as DoPT secretary.
He was appointed as the chief of the government's head-hunting agency, the PESB, in November 2016.
Kothari has served in various positions both at the Centre and the state cadre.
Malik is at present a Distinguished Fellow at Observer Research Foundation (ORF), a policy think tank. He is head of the ORF's Neighbourhood Regional Studies Initiative.
His work focuses on Indian domestic politics and foreign/trade policy, and their increasing interplay.
Also, on the broader process of globalisation and how it is influencing policy choices in not just the economy but in the social sector spheres such as health, education and urbanisation.
A journalist for 20 years, Ashok Malik is a columnist for several leading Indian and international publications.
He has co-authored and authored books including India: Spirit of Enterprise. It encapsulates the story of the growth of India's leading private sector industries since 1991, and their role in the Indian economy, according to his profile on the ORF's website.