Accompanied by his wife Duchess of Cornwall, Camilla Parker Bowles, Charles landed here this afternoon.
The visit is a part of their 10-day tour of four nations -- Singapore, Malaysia, Brunei and India.
"A relationship marked by mutual respect and strong bonds of friendship. Prime Minister Modi welcomed Their Royal Highness, the Prince of Wales and the Duchess of Cornwall at Hyderabad House, wide ranging issues on strengthening bilateral cooperation were discussed," external affairs ministry spokesperson Raveesh Kumar tweeted.
India is the third largest investor in the UK and the second largest international job creator in the UK.
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The UK is the third largest inward investor in India, with a cumulative equity investment of USD 24.37 billion for the period April 2000June 2017.
This is the ninth visit of the Prince of Wales to India since 1975, the last being in 2013.
According to officials, the invitation to attend CHOGM has been issued by the secretary general of Commonwealth to all members nations and the issue was discussed in today's meeting.
"The elephant family sculptures will be taken to Mumbai to raise awareness of the charity's mission to help protect Asian elephants," the Clarence House said in another tweet.
The Indian diaspora in the UK is one of the largest ethnic minority communities there, with the 2011 census recording approximately 1.5 million people of Indian-origin in the UK, contributing 6 per cent to the country's GDP.