Chief of Defence Staff Gen Bipin Rawat, his wife and 11 others died after the Mi-17V5 helicopter came down in hills near Coonoor city on Wednesday morning.
One survivor is being treated for his injuries in hospital.
Gen Rawat, 63, was appointed India's first-ever Chief of Defence Staff in January 2019.
This brought together the Army, the Navy and the Air Force, and Gen Rawat had been in charge of a range of operations including in Indian-administered Kashmir.
The Indian Air Force said it had ordered an investigation into the accident, which happened in foggy weather. A cabinet security committee is holding an emergency session, chaired by Prime Minister Narendra Modi.
On Twitter, Mr Modi said: "[Gen Rawat] brought with him a rich experience of serving in the Army. India will never forget his exceptional service.
"A true patriot, he greatly contributed to modernising our armed forces and security apparatus. His insights and perspectives on strategic matters were exceptions. His passing away has saddened me deeply."
The Russian-made Mi-17V5 military helicopter had just taken off from an army base in Sulur, and was heading for Wellington town, less than 100km (62 miles) away, where Gen Rawat was due to visit the Defence Services Staff College (DSSC).
On board with Gen Rawat and his wife were seven other military passengers and five crew members, including the pilot.
The sole survivor of the crash was a captain working at the DSSC.
One eyewitness told local media he heard a number of "terrible loud sounds" before seeing the helicopter fall from the sky.
"I saw the helicopter coming down... it hit one tree and was on fire," Krishnaswamy, a nearby resident, told The News Minute. "There were plumes of smoke when I ran over. In minutes, the fire was higher than my house."
Rescue efforts were hampered due to the crash site's hilly location, which is thick with vegetation.
Gen Rawat, who was born on 16 March 1958 in the northern state of Uttarakhand, had the reputation of being a tough soldier and an inspiring commander. In recent months, the general was focusing on modernising the military.
Although the Mi-17V5 is among the most sophisticated military transport helicopters, India's ageing air force fleet is often blamed for a high number of crashes.
Former army chief J J Singh said it was "a safe, proven helicopter", adding that he himself had travelled on it in difficult situations.