"The India-New Zealand relationship will only continue to grow, and this visit will help drive New Zealand's political and commercial partnership with the world's third-largest economy," Key said.
"Along with further strengthening New Zealand's political, security and economic connections with India, my meeting with Prime Minister Modi will be an opportunity to discuss his efforts to reform India's economy and how New Zealand can be part of India's growth."
The business delegation is about 35-strong and includes representatives from Fonterra, the India New Zealand Business Council, Pipfruit NZ, universities, Zespri and National MPs Mark Mitchell and Kanwaljit Singh Bakshi.
Mike Loftus, executive chair of CricHQ, will be on the trip. McCullum is an investor in the Cricket app and data company.
New Zealand made India the subject of its first "NZ Inc" strategy in 2011, with the goal of shipping $2 billion of goods to India by 2015.
Instead, the value of goods exported to India annually has fallen, from $900 million five years ago to $637 million last year.
Negotiations for a free trade agreement kicked off in April 2010 and have gone through 10 rounds without a result.
A report on the India-NZ relationship released on Saturday by the Asia New Zealand Foundation noted that "if divisions over trade policy qualify as a test of friendship, India and New Zealand have been well tested".
With India now the world's fastest-growing economy, New Zealand is keen to stop the testing - Key in May said he pushed "pretty hard" on the deal when he met Indian President Pranab Mukherjee in Auckland.
One issue noted in the Asia New Zealand report is that New Zealand has very little left to concede on tariff reductions.
