"Chief Minister Jayalalithaa was a leader dearly loved by her people. I express my condolences to her loved ones and the people of Tamil Nadu," Sirisena said.
Former Sri Lankan president Mahinda Rajapaksa also offered his condolences, saying "she captured the hearts of India's Tamil community".
Rajapaksa, during his presidency, invited Jayalalithaa to visit Sri Lanka to witness the post-war conditions.
Jayalalithaa had a checkered relationship with Sri Lanka.
While the Sinhala majority supported her strong anti-LTTE sentiments, they did not favour her for her pro-Tamil nationalist stance.
Jayalalithaa, hospitalised since September 22, suffered a cardiac arrest on Sunday and passed away late last night in Chennai.