From http://www.nps.gov/whho/PPSth/boysctmem/index.htm:
During the 50th Anniversary Year of Scouting (1959), a proposal was made to establish the memorial on a site in Washington, D.C. Lyndon B. Johnson, who was the Senate majority leader at the time, introduced the measure to the Senate. The memorial was eventually unveiled in a ceremony on November 7, 1964.
Thumbnail from Google Earth.