The appointment of executive directors will either be on deputation or contractual basis, for an initial period of three years, Sebi said.
While Padmanabhan's tenure with Sebi has already ended, Bhushan's term is scheduled to end soon.
Bhushan is presently serving as executive director in Sebi's Integrated Surveillance Department as well as Office of Investor Assistance and Education.
An advertisement regarding the recruitment process has been uploaded on Sebi's website. The last date for receiving the applications is November 25, 2016.
Currently, Sebi has seven executive directors, who report to Sebi whole-time member S Raman.
According to the regulator's organisation structure, these EDs include S Ravindran, S V Murali Dhar Rao, P K Nagpal, J Ranganayakulu and Ananta Barua.