The community was named after David A. Pennicuick, a railway official and accountant. Like many small settlements across rural Alberta, its establishment was tied to the expansion of the region's railway lines.

A post office officially opened in the area on May 1, 1913. Early residential and commercial development accelerated mid-century, highlighted by the construction of the Dapp Hotel in 1948 and local housing development beginning around 1945.

Dapp has historically functioned as a tight-knit agricultural community. A notable milestone in its agricultural history occurred in 1985, when the Alberta Wheat Pool constructed one of the last traditional wooden grain elevators built in the province right in Dapp. Like many small prairie farming hamlets, Dapp’s population peaked mid-century (reaching around 77 residents in 1951) before slowly declining as rural demographics shifted. The town derives its name from the initials of David A. Pennicuick, a railroad official.