Long before the arrival of Europeans in the Americas, one of the world’s largest rainforests teemed with people who transformed the woods around them, according to archaeologists who have found new evidence of farms, settlements and roads buried beneath the flora of Brazil’s Amazon Basin.

A retiree poring over online satellite images led archaeologists to the ancient earthworks, the most recent in a series of finds made possible by satellite imagery, airborne radar, and drone-mounted cameras that are making ecologists and...