May, 60, will be in India between November 6 and 8 on the invitation of Modi.
She will be accompanied by her international trade minister Liam Fox and a business delegation drawn from regions across the UK as "examples of the best of British business".
"The relationships between our two countries are strong, and the Indian diaspora plays a vital role in our national life," May said.
"As we leave the European Union, we have the chance to forge a new global role for the UK - to look beyond our continent and towards the economic and diplomatic opportunities in the wider world. I am determined to capitalise on those opportunities and as we embark on the trade mission to India, we will send the message that the UK will be the most passionate, most consistent, and most convincing advocate for free trade," May said.
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The India-UK partnership has moved into a new era, with Britain voting to leave the European Union (EU) in a referendum in June and leading to the resignation of then prime minister David Cameron.
May will land in New Delhi, where she will inaugurate the India-UK TECH Summit alongside Modi.
The TECH Summit, described as South Asia's largest technology conference, will provide a platform for promoting technology-intensive trade between the two countries.
May also sought to set her trade delegation apart from the
"In the past, the focus of trade delegations has been big businesses, but I want to take a new approach that recognises the full range of British business. So this time we will be focussing on small and medium sized businesses - and, importantly, the delegation will include representation from every region of the UK.
"I want to create an economy that truly works for everyone - and this new approach to international trade missions will help achieve just that," May said.
The small and medium enterprises accompanying her will include Geolang, an innovative cyber security company based in Cardiff, Torftech, a creative energy company based in the South-East, and Telensa, a company focussed on smart city solutions based in Cambridge.
May has repeatedly named India among the priority countries to strike trade deals as the UK leaves the EU following the June 23 referendum.
The visit will mark her second trip to India.
In her capacity as UK Home Secretary, she previously visited New Delhi and Hyderabad on November 27-29, 2012, where she visited the National Police Academy and held talks with ministers and the National Security Adviser on bilateral security cooperation.