The names were cleared by President Pranab Mukherjee, who is the Visitor to the IITs, said highly placed sources in the HRD Ministry.
Raja Kumar is a faculty in IIT-Kharagpur while Bhattacharya is professor of Computer Science and Engineering at IIT-Bombay and Das a professor of Mechanical Engineering at IIT-Madras.
Their appointments come after the ministry had held a marathon round of selection process on March 22 and interviewed 36 IIT faculties for the three posts.
The interview on March 22 was called afresh after the ministry had quashed an earlier selection process to appoint the new directors for the three IITs.