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HDFC Bank said its board will meet in "in due course" to approve Mr Jagdishan's appointment.
HDFC Bank shares jumped as much as 5.78 per cent to Rs 1,059.90 apiece on the BSE after the announcement. At 12:11 pm, the HDFC Bank stock traded 4.32 per cent higher at Rs 1,045.20 on the bourse, outperforming the benchmark S&P BSE Sensex index which was up 1.67 per cent. (Track HDFC Bank Shares Here)
After 26 years at the helm, Mr Puri is set to retire when he turns 70, the age limit set by the RBI for private bank chiefs.
The lender had shortlisted three names for his successor in April.
Mr Jagdishan will face the challenge of maintaining HDFC Bank's relatively high asset quality and loan growth as the coronavirus pandemic sends the country's economy into a deep slump.
The country's biggest lender by market value has managed to skirt a two-year-old shadow-banking crisis under Mr Puri.
Mr Jagdishan has an overall experience of 29 years. He joined HDFC Bank in 1996 as a manager in the finance function, became business head-finance in 1999, and was appointed chief financial officer in 2008.
He has played a critical role in supporting the growth trajectory of HDFC Bank. Mr Jagdishan has led the finance function and played a pivotal role in aligning the organisation for achieving the strategic objectives over the years.
He heads the functions of finance, human resources, legal and secretarial, administration, infrastructure, corporate communications and corporate social responsibility.
He is a science major with specialization in physics. Mr Jagdishan is a chartered accountant by profession, and holds a Master's degree in economics of money, banking and finance.