Support worth about £200m ($319m) will be phased out between now and 2015 and the UK's focus will then shift to offering technical assistance.
Ms Greening said the move, which will be popular with Tory MPs, reflected India's economic progress and status.
Giving his reaction, India's foreign minister Salman Khurshid said: "Aid is the past and trade is the future."
But charities described the move as "premature" and warned it would be the poorest who suffered.
Until last year, when it was overtaken by Ethiopia, India was the biggest recipient of bilateral aid from the UK, receiving an average of £227m a year in direct financial support over the past three years.
But the UK's support for India, one of the world's fastest-growing economies, has been a cause of concern among Conservative MPs, many of whom believed that the UK should not be giving money to a country which has a multi-million pound space programme.
Ministers have defended the level of financial help in the past on the basis of the extreme poverty that remains in rural areas and historical colonial ties between the two countries.
Ms Greening has been conducting a review of all financial aid budgets since taking over the role in September and visited India earlier in the week to discuss existing arrangements.
'Hitting the vulnerable'
Labour MP Keith Vaz, a former chair of the Indian-British parliamentary group, said the government needed to reassure its Indian counterpart that their bilateral relationship was still a priority.
"Although undoubtedly India has progressed in the past 20 years, there are still an estimated 360 million people surviving on less than 35 pence per day," he said.
"In withdrawing our aid to India, which will clearly only affect the most vulnerable, we need to see the minister's plan for how she will work with other organisations to make sure the gaps we are creating will be filled."
War on Want, which campaigns to end global poverty, said aid should not just stop because India had become a middle-income country.
Financial support needed to be "smarter" and geared towards supporting "progressive movements" capable of bringing about political change and tackling growing inequality, the pressure group said.
The UK government is increasing the overall overseas development budget to meet a longstanding international commitment to spend 0.7% of national income on aid.
At the same time, it wants to re-align its expenditure to focus on the poorest countries and those scarred by recent conflict.
