MUMBAI—India is bracing for a dramatic but risky overhaul of the country’s tax system that authorities hope will draw millions of businesses into their tax net and boost the economy.

The initiative, set to kick off on July 1, aims to streamline India’s cumbersome network of state and federal levies and ease commerce across state borders.

It is a big part of a larger effort, including the cancellation of large-denominated currencies last year, to improve tax collection from companies that make up India’s huge informal economy. Some estimate the new system will add nearly 1 percentage point to India’s GDP growth within a few years.

But the risks could drag on short-term economic growth, experts say. Among the hurdles are getting millions of companies to register, educating them on how to file online, poor internet connections and widespread tax avoidance. The design of the new nationwide Goods and Services Tax—which replaces a value-added tax and other levies—also is more complex than many expected.

A chaotic rollout could roil an economy still hobbled by a cash shortage caused by the elimination of the bank notes in November.