Dikshit passed away at a private hospital here following a cardiac arrest. She was 81.
President Ram Nath Kovind and Prime Minister Narendra Modi were among the first to condoled the demise of Dikshit.
Kovind said she had transformed the national capital in her tenure.
"Sad to hear of the passing of Sheila Dikshit, former Chief Minister of Delhi and a senior political figure. Her term in office was a period of momentous transformation for the capital for which she will be remembered. Condolences to her family and associates," the President said in a tweet.
Modi too said that Dikshit made a noteworthy contribution to Delhi's development.
"Deeply saddened by the demise of Sheila Dikshit. Blessed with a warm and affable personality, she made a noteworthy contribution to Delhi's development. Condolences to her family and supporters," Modi tweeted.
Condoling the demise of the senior Congress leader, Home Minister Amit Shah said, "Sad over the demise of former Chief Minister Sheila Dikshit. My heartfelt condolences to the family members and her supporters. May god give strength to her family in this hour of grief and lasting peace to the departed soul."
Defence Minister Rajnath Singh tweeted: "The passing away of former Chief Minister of Delhi, Smt Sheila Dixit is deeply saddening. She was a tall Congress leader known for her congenial nature. Sheilaji was widely respected cutting across party lines. My thoughts are with her bereaved family & supporters. Om Shanti!"
Nitin Gadkari, Minister for Road Transport and Highways, said, "Saddened to hear the news about the demise of former Chief Minister of Delhi Sheila Dikshit. Her contributions in the development of Delhi will always be remembered. My condolences to the family. May her soul rest in peace."
Former External Affairs Minister Sushma Swaraj said, "I am sorry to know about the sudden demise of Sheila Dikshitji. We were opponents in politics but friends in personal life. She was a fine human being."
Veteran CPI-M leader Sitaram Yechury tweeted, "Deepest condolences on the death of Mrs Sheila Dikshit. She has made a tremendous contribution to the city of Delhi and millions of its people. Her absence will be deeply felt. Personally too, it is a very sad day."
Minister of Information and Broadcasting Prakash Javadekar said, "Saddened over the demise of senior Congress leader Sheila Dikhsit. She was loved and respected by all the parties. May god give strength to the family in this hour of grief and peace to the departed soul."
West Bengal Chief Minister Mamata Banerjee said, "Deeply saddened at the passing away of Sheila Dikshitji. When I became the MP, she was the Parliamentary Affairs Minister. She always maintained good relations with me. We will all really miss her."
( With inputs from IANS )