America's Greenbelt Towns came about as an extrapolation of urban planning concepts put forward by Great Britain's Sir Ebenezer Howard. In his book "To-Morrow: A Peaceful Path to Real Reform" (1898), the bucolic utopian "Garden City" was envisaged.
Graphic from "Greenbelt Towns" brochure / US Government Printing Office / 1936

According to Howard, people should be residing in communities that combined the best of town and country life. Green suburbs, surrounded by a permanent belt of forested land, would eschew many of the pitfalls of city life, such as poverty, overcrowding, low wages, inadequate sanitation, pollution and disease. In many ways, these trend-setting communities espoused the tenets of today's "New Urbanism" movement. 
Photo from Wikipedia / "Marnanel"

Letchworth, the first of Ebenezer Howard's Garden Cities, was started -in Hertfordshire County, Great Britain- in 1903. Across the pond, Radburn, New Jersey, America's prototype garden suburb, broke ground in 1929. Seen above is the Radburn Plaza Building; commercial center of the Bergen County planned city.
Photo from Library of Congress / Carl Mydans