Tillerson landed at Indira Gandhi International Airport late Tuesday night local time, and Wednesday will hold meetings with Indian officials, including Prime Minister Narendra Modi.
A rising and increasingly assertive China, as well as America's future plans for war-torn Afghanistan, are among the issues that are likely to top the agenda, say analysts.
Here are the key issues to watch out for.
Although he isn't visiting Beijing on this trip, China is set to be a key talking point during the secretary of state's visit to India. Tillerson indicated as much last week, when he contrasted India with China in a speech in Washington.
"The driving force of our close relationship rests in the ties between our peoples -- our citizens, business leaders, and our scientists. ... We'll never have the same relationship with China, a nondemocratic society, that we can have with a major democracy," he said on October 18.
The warm words for New Delhi come as China carves out its One Belt, One Road project, economic and infrastructure projects that span more than 68 countries across Europe, Asia and Africa.
"The rise of a more capable and assertive China remains the single most important driver of the growing partnership between Washington and Delhi," Constantino Xavier, a fellow at Carnegie India, a think tank, said in an email.
The friendly tone toward New Delhi also predates the Trump administration, as the US sought to cultivate India as a bulwark against China.
"There's a huge element of continuity in all of this. All presidents from Bill Clinton onwards, all of them have strongly supported an India-US relationship," said Ajai Shukla, a defense analyst and former Indian military officer based in New Delhi. "This is equally true of Indian prime ministers, irrespective of ideology and irrespective of strategic orientation."
Another major issue: Afghanistan, which remains in the grip of a bloody, 16-year conflict.
In August, speaking at Fort Myer in Arlington, Virginia, US President Donald Trump renewed the US military commitment in Afghanistan, while also calling on India and other regional players for more support in bringing stability to the country.
"We appreciate India's important contributions to stability in Afghanistan, but India makes billions of dollars in trade from the United States and we want them to help us more with Afghanistan, especially in the area of economic assistance and development," he said.
India has a longstanding partnership with Afghanistan, supplying about $2 billion in aid, namely in developmental and infrastructural projects.
But New Delhi is not about to get involved militarily, says Shukla. "Every statement from both sides has been oriented towards the understanding that India will step up humanitarian aid and developmental projects."
India's longtime rival Pakistan, where Tillerson stopped on Tuesday, is also likely to feature in his conversations in New Delhi.
Although Trump called out Pakistan for giving "safe haven to agents of chaos, violence and terror" in his speech in August, he recently appeared to shift tack, tweeting effusively about the relationship with Islamabad after Pakistani forces helped rescue an American woman, her Canadian husband and their three children held captive by a Taliban affiliated group.
As Tillerson headed to South Asia, there was also news that Pakistan was extending the detention of Hafiz Saeed, the alleged mastermind behind the devastating 2008 Mumbai terror attacks, sidestepping a potential political banana skin that could have erupted during Tillerson's visit.
"[His arrest] took place because of a realization within the Pakistan army that Hafiz Saeed was endangering Pakistan's insistence that it was not supporting terrorist groups. What we saw was a change in the Pakistani strategic projection," Shukla said. "The factors that are driving this, which is Trump's pressure, India's pressure, all of these issues are keeping Pakistan towards that change in strategic orientation."