In the days before the 1950s creation of the Dwight D. Eisenhower National System of Interstate and Defense Highways--better known as the Interstate system--standardized highway signs on the U.S. highway system, signs were mostly warning and regulatory signs. Guide and other informational signs were far less standardized.
Before the 1950s, California had the largest system of highways in the nation. Its highways included black guide signs with white letters, for a contrast that was considered easy to see, day or night. The 1954 MUTCD adopted this kind of highly visible guide sign for federal highways, but changed the background color from black to a light-reflective green, which also offers excellent visibility.
In the early 1970s, MUTCD specified green guide signs on all highways within the United States, not just the federal Interstate system. Strictly speaking, the green signs on state highways aren't mandatory, but a state that doesn't use them--or the other types of signs specified by MUTCD--loses a significant share of its federal highway-aid funding.
The current MUTCD (2009 edition) specifies that "guide signs on freeways and expressways, except as otherwise provided in this Manual, shall have white letters, symbols, arrows and borders on a green background." The MUTCD also specifies exactly which shade of green that is, according to standard definitions of color.
Not all informational highway signs are green under the MUTCD scheme. Brown signs with white letters, for example, notify drivers of points of interest ahead (parks, historic sites, campgrounds), while blue signs with white letters indicate services ahead, such as gas, food or rest areas.