Rajendran would succeed H N Sinor, whose term ends in September.
He took charge of Andhra Bank in 2013. Prior to that, Rajendran was executive director of Bank of Maharashtra and has also worked with Corporation Bank for several years.
The Association of Mutual Funds of India (AMFI) started searching for the new CEO in May and had set up a three-member committee to find the successor for Sinor.
The search panel comprised of AMFI chairman Sundeep Sikka, who is also managing director and chief executive of Reliance MF, HDFC MF managing director Milind Barve and Birla Sun Life MF chief executive A Balasubramanian.
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During Sinor's tenure, the mutual fund industry has dealt with sweeping regulatory changes.
Among the initiatives taken during his term, AMFI has put one per cent cap on upfront commission paid to distributors and initiated investor awareness campaign.
Sinor is a former ICICI Bank executive and chief executive of the Indian Banks' Association.
Commenting on the development, Sikka said, "We welcome Rajendran to AMFI and wish him all the very best. We also thank Sinor for his role. During his tenure, he took several initiatives for the mutual fund industry."
It also serves as a self-regulatory body for mutual funds.