Bhat is currently leading the group's watches and jewellery firm, Titan Company, Tata Sons said in a statement.
On the other hand, Agrawal had joined the Tatas as Group Chief Financial Officer in July from the Aditya Birla Group, where he was Head of Strategy, it said.
Agrawal brings deep capital market knowledge and valuable cross industry experience to the Tata group, the statement added.
Tata Sons Chairman N Chandrasekaran said: "We welcome Bhaskar and Saurabh to the Board of Directors. The Board will benefit from the tremendous experience and knowledge of these professionals in multiple domains."
Tata group veteran Ishaat Hussain had recently retired from the board.