Home Minister Amit Shah and BJP chief J.P. Nadda also expressed condolences over the sudden demise of CDS Rawat and 12 other onboard the ill-fated chopper.
In a series of tweets, President Kovind said, "I am shocked and anguished over the untimely demise of Gen Bipin Rawat and his wife, Madhulika ji. The nation has lost one of its bravest sons. His four decades of selfless service to the motherland was marked by exceptional gallantry and heroism. My condolences to his family."
"It's deeply painful for me to learn of the loss of lives in the chopper crash. I join the fellow citizens in paying tributes to each of those who died while performing their duty. My heartfelt condolences to the bereaved families," the President said in another tweet.
Expressing his grief, Prime Minister Modi said in a series of tweets, "I am deeply anguished by the helicopter crash in Tamil Nadu in which we have lost Gen Bipin Rawat, his wife and other personnel of the armed forces. They served India with utmost diligence. My thoughts are with the bereaved families."
"Gen Bipin Rawat was an outstanding soldier. A true patriot, he greatly contributed to modernising our armed forces and security apparatus. His insights and perspectives on strategic matters were exceptional. His passing away has saddened me deeply. Om Shanti," the Prime Minister added.
Modi also pointed out that India will never forget General Rawat's exceptional service.
"As India's first CDS, Gen Rawat worked on diverse aspects relating to our armed forces, including defence reforms. He brought with him the rich experience of serving in the Army. India will never forget his exceptional service," Modi said.
Sharing his grief, Amit Shah said, "A very sad day for the nation as we have lost our CDS, General Bipin Rawat Ji, in a very tragic accident. He was one of the bravest soldiers, who served the motherland with utmost devotion. His exemplary contributions and commitment cannot be put into words. I am deeply pained."
"I also express my deepest condolences on the sad demise of Mrs Madhulika Rawat and 11 other Armed Forces personnel. My thoughts are with the bereaved families. May God give them the strength to bear this tragic loss. Praying for the speedy recovery of Gp Capt Varun Singh," the Home Minister said.
Expressing his condolences to the bereaved families, Union Education Minister Dharmendra Pradhan tweeted: “"Pained at the passing away of the Chief of Defence Staff Shri Bipin Rawat, his wife Mrs. Madhulika Rawat and 11 others on board the IAF helicopter that crashed near Coonoor today. General Rawat’s demise is a loss for the country. My sincerest condolences to the families who lost their loved ones."
(With inputs from IANS)