Upon his arrival in Delhi, Premier Li will hold talks with Prime Minister Manmohan Singh, followed by dinner at the Indian leader's residence.
Border tensions and trade ties are expected to be among the issues discussed by the two men.
The neighbours are the world's two most populous countries.
Beijing hopes the visit will help build trust and a new strategic partnership to the benefit of both countries, China's official news agency Xinhua said.
Delhi thought "very highly" of Mr Li's decision to make India his first foreign stop and the aim of the talks was to "enhance trust", Indian foreign ministry spokesman Syed Akbaruddin said.
A decades-long border dispute flared up last month after India accused Chinese troops of crossing the countries' de facto border in the Himalayas.
The dispute over the territory in the Ladakh region has dogged the two countries since the 1950s.
Boosting trade ties is also expected to dominate the talks. China is already one of India's top trading partners and both countries have already agreed a new $100bn (Â£65bn) bilateral trade target for 2015.
Premier Li will spend three days in India before travelling on to Pakistan, Switzerland and Germany.
China's Premier Li Keqiang is travelling to India in the first stop of his maiden foreign trip since taking office.