The deal was reached Tuesday night, Japan time, Son said at a news conference following the release of SoftBank's earnings report.
Son did not disclose further details of the deal. Confirmation of the transaction ends much speculation that the U.S. retail giant would strike a deal with the Indian start-up.
SoftBank is currently one of the largest shareholders in Flipkart. According to reports, the tech giant will sell its entire stake to Walmart as part of the deal.
Homegrown internet retailer Flipkart has a user base of 100 million, according to the company's website. India, which has a population of more than 1.3 billion, is seeing rapid growth in its digital economy with the emergence of e-commerce start-ups like Snapdeal and Paytm.
The investment sees Walmart take on U.S. e-commerce giant Amazon in a key growth market for the company. In 2016, Amazon CEO Jeff Bezos announced that his firm would invest $3 billion in India. Amazon reportedly made its own bid for a majority stake in Flipkart.
Walmart's deal with Flipkart follows a merger between its U.K. supermarket brand Asda and rival Sainsbury's, a tie-up that presented a significant competitive challenge to Britain's dominant grocer Tesco.