Wang said his two-day visit as a special envoy of President Xi Jinping was to "cement our existing friendship and explore further cooperation".
"China is ready to work with our Indian friends for an even brighter future of our strategic and cooperative partnership," Wang said in an interview with The Hindu newspaper published yesterday.
Despite his hardline nationalist reputation, Modi has been making overtures to traditional rivals China and Pakistan since his Bharatiya Janata Party (BJP) swept to power last month.
The new Indian leader has invited Xi to visit, and Wang told the newspaper that the president has agreed to come later this year.
Wang, who arrived early yesterday, shook hands with India's new foreign minister, Sushma Swaraj, and smiled and waved to media on the steps of government offices before heading inside.
The talks are expected to focus on strengthening economic ties rather than detailed discussions on a border dispute between the nuclear-armed neighbours that has soured ties for decades.
Wang is coming "to engage with our leadership and we will take it from there", India's foreign ministry spokesman Syed Akbaruddin told a news briefing last week.
Modi, a frequent visitor to China before he became premier to seek investment for his home state of Gujarat, has pledged increased foreign investment to help revitalise the economy.
China is India's biggest trading partner with two-way commerce totalling close to US$70 billion. But India's trade deficit with China has soared to more than US$40 billion from just US$1 billion in 2001-2002, Indian figures show.
Relations however are still dogged by mutual suspicion - a legacy of a brief, bloody border war in 1962 over the Indian northeastern state of Arunachal Pradesh which China claims as its own.
Wang acknowledged the border tensions, but said the two countries have "much more strategic consensus than differences and cooperation is our top priority".
"The boundary question is indeed a difficult one, but with strong will and resolve, we will eventually find a solution," he told The Hindu.
Shi Yinhong , a foreign relations professor at Renmin University, said India was important to China because of its size, and for strategic and economic reasons. But Modi's attitude towards Beijing was still uncertain.
"He is very serious about the market economy, and may wish to improve trade and economic ties with China," Shi said. "But he is also the head of a party that has been hawkish over the two countries' territorial dispute."
Jia Xiudong , a senior research fellow at the China Institute of International Studies, said both Beijing and New Delhi were apparently trying to manage the territorial dispute and prevent it from derailing bilateral ties.
Ranjit Gupta, a member of the Indian Security Advisory Council of the US-India Institute, a Washington-based think tank, said Wang's visit augured well for both countries.
"China has gone all out to woo the new Indian government, which is a great gesture," he said.