The media said Mr Sharif's open support for stronger ties between the two countries was reason for hope.
Unofficial results suggest a big lead for Mr Sharif's Muslim League (PML-N), though he may need support to govern.
Indian PM Manmohan Singh has congratulated Mr Sharif for his win and invited him to visit India.
The Hindu newspaper said the election had been "Pakistan's vote for change".
"Where he [Mr Sharif} gives most hope is in his strong and unambiguous articulation of better India-Pakistan relations, though this will depend on his stated determination to correct the civil-military imbalance, and reclaim the national agenda from the security establishment," the newspaper said.
"Whether he can succeed is another question, but India will be hoping he will."
The Indian Express said Mr Sharif has "persuasively presented himself as a peacemaker, pointing to his previous stints in government to give confidence that he will pick up the threads of dialogue with India".
Hindustan Times said "India has genuine reason to be pleased" by the results of the election.
The newspaper described Mr Sharif as the "co-author of the Lahore bus peace process" and one who "has been far more willing to walk the India talk - even in the teeth of strong military opposition".
"Stronger Sharif bodes well for India", said The Times of India newspaper.
"India's best bet would be for the new Pakistan government to focus on opening up trade and economy," the newspaper said.
Mint newspaper said Mr Sharif's win was "likely to boost economic ties with India, but improving diplomatic relations will mainly depend on the stance of the country's armed forces".
Ties between the two countries came under strain earlier this year following military tensions in the disputed region of Kashmir.
Claimed by both countries, Kashmir has been a flashpoint for over 60 years and two wars have been fought over it.
Peace negotiations resumed last February after a four-year break following attacks by Pakistan-based militants in Mumbai in 2008.
India's media has hailed former Pakistani PM Nawaz Sharif's win in general elections and said it was good for the peace process with India.