Walmart’s e-commerce unit, Flipkart Online Services, signed a pact with tycoon Gautam Adani’s conglomerate to build one of the largest retail warehouses in India as the US giant gears up to battle Amazon.com and home-grown rivals in the South Asian nation.

The partnership marks the entry of Adani, India’s fastest-rising billionaire, into the three-way fight for domination of India’s online shopping space. Up against the Walmart-Adani alliance is not just Amazon, but also Reliance Industries, the conglomerate owned by Mukesh Ambani, India and Asia’s richest man...