After lagging behind other countries for years, commercial drones in the U.S. are expected to begin limited package deliveries within months, according to federal regulators and industry officials.

The momentum partly stems from stepped-up White House pressure, prompting closer cooperation between the government and companies such as Amazon.com Inc. seeking authorizations for such fledgling businesses. The upshot, according to these officials, is newfound confidence by both sides that domestic package-delivery services finally...