NEW DELHI—In a surprise announcement Tuesday night, Prime Minister Narendra Modi said India will replace its largest-denomination bank notes with newly designed ones, a move aimed at curbing corruption, thwarting counterfeiters and dredging up what could be billions of dollars of taxable income currently stashed in the underground economy.

The new 500- and 2,000-rupee notes, worth around $7.50 and $30 respectively, will begin to circulate soon. Current 500- and 1,000-rupee bills ceased being legal tender Wednesday but can...