It marks Mr Biden’s first visit to the South Asian nation since he took office. He flew into Delhi's Indira Gandhi International Airport aboard Air Force One shortly before 7pm.
Mr Biden met Mr Modi at his newly built residence, Vatika – meaning “garden” – which was decorated with elaborate lamps and burbling fountains.
“Our meeting was very productive. We were able to discuss numerous topics which will further economic and people-to-people linkages between India and USA,” Mr Modi wrote on X, formerly Twitter.
“The friendship between our nations will continue to play a great role in furthering global good.”
The White House said the two leaders reaffirmed the close partnership between the countries.
“The leaders re-emphasised that the shared values of freedom, democracy, human rights, inclusion, pluralism and equal opportunities for all citizens are critical to the success our countries enjoy and that these values strengthen our relationship,” it said.
The leaders of the world’s largest and oldest democracies met three months after Mr Modi's state visit to the US in June.
Washington and New Delhi have deepened their relationship in recent decades following a long period of distrust between the two countries during the Cold War era, when India was seen as a close friend of Moscow.
Several deals in the sectors of defence, renewable energy, technology collaboration, health care and climate change were signed during Mr Modi’s visit, including a deal with Micron Technology to build a $2.75 billion semiconductor assembly and test facility in India.
Mr Modi’s government has been aspiring to make India a global chip manufacturing hub and is looking to attract major producers as China also works towards becoming a technological power.
India currently imports about 80 per cent of its required semiconductors.
The White House said the two leaders reiterated their support for building resilient global semiconductor supply chains. It said a multi-year initiative will result in US firm Microchip Technology investing $300 million into expanding its research presence in India, with Advanced Micro Device investing $400 million in the country over the next five years.
The two countries will also work closely on defence in emerging domains such as space and artificial intelligence, the White House said.
Mr Biden lauded Mr Modi for India's G20 presidency and said the summit would advance shared goals of sustainable development.
The US President reaffirmed his support for a reformed UN Security Council with India as a permanent member and welcomed the country's candidacy for a non-permanent seat on the council in 2028-29.
India is one of the founding members and an active participant in the UN but does not have a permanent Security Council seat, with the US, the UK, China, Russia and France do.
Mr Modi also held talks with his Bangladeshi counterpart Sheikh Hasina and Mauritian Prime Minister Pravind Jugnauth on Friday.
He will hold 15 bilateral meetings with world leaders, including UAE President Sheikh Mohamed, who arrived in New Delhi on Friday.
World leaders will discuss major issues related to the global economy, financial stability, climate change mitigation and sustainable development at the summit.