In 1882, Enrico Piaggio purchased land in Sestri Ponente (Genoa) to set up a timber yard. Two years later, in 1884, his 20-year-old son, Rinaldo Piaggio (1864–1938), founded Piaggio & C. The company initially built locomotives and railway carriages but in 1917, towards the end of World War I, Rinaldo Piaggio turned to the military sector. To begin, the company produced MAS anti-submarine motorboats, aeroplanes and seaplanes under AnsaldoMacchiCaproni, and Dornier licenses but later progressed to vehicles constructed according to Piaggio's own drawings.

Between 1937 and 1939 Piaggio achieved 21 world records with its aircraft and engines built at the company's new factory in Pontedera, culminating in the four-engine Piaggio P.108 bomber.

Rinaldo died in 1938, by which time Piaggio was owned by multiple shareholders within the family, along with the entrepreneur Attilio Odero. Management of the company passed to his sons Enrico and Armando.

By 1940 Piaggio was manufacturing trains, nautical fittings, aircraft engines, aeroplanes, trucks, trams, buses, funiculars and aluminium windows and doors. The Pontedera plant was destroyed by Allied bombing and production activities were relocated to the Biella area. After the war, Enrico Piaggio decided to diversify the company's activities outside the aeronautical industry to address a perceived need for a modern, affordable mode of transport for the Italian mass market. The first attempt, based on a small motorcycle made for parachutists, was known as the MP5 and nicknamed the "Paperino" (the Italian name for Donald Duck) because of its strange shape. Ultimately Enrico Piaggio did not like it and asked Corradino D'Ascanio to redesign it.

D'Ascanio, an aeronautical engineer responsible for the design and construction of the first modern helicopter by Agusta, was not naturally enthusiastic about motorcycles, judging them to be uncomfortable and bulky, with wheels that were difficult to change after a puncture. When asked to design a motorcycle for Ferdinando Innocenti, D'Ascanio had come up with a step through scooter design but D'Ascanio and Innocenti disagreed over use of a pressed steel frame rather than tubular, so D'Ascanio took his design to Piaggio. Innocenti would ultimately use D'Ascanio's original design for their Lambretta scooter.

Piaggio asked D'Ascanio to create a simple, robust and affordable vehicle. The motorcycle had to be easy to drive for both men and women, be able to carry a passenger, and not get its driver's clothes dirty. The engineer's drawings proved a significant departure from the Paperino. With the help of Mario D'Este he prepared the first Vespa project, manufactured at Piaggio newly-rebuilt Pontedera headquarters in April 1946. Piaggio launched the Vespa (Italian for "wasp") and within ten years more than a million units had been produced. The Italian language gained a new word, "vespare", meaning to go somewhere on a Vespa.