"When we have the U.S. Postal Service making the announcement that there are 50,000 suggestions per year, out of which 20 are selected - if that isn't the very embodiment of the American Dream, well, I don't know what is," Sinatra said at a ceremony in Manhattan.
"He was a fellow off the streets of Hoboken, N.J.," the son said, adding that the late singer's father was a firefighter and his mother a homemaker.
The 42-cent Sinatra stamp went on sale Tuesday in three places, including New York, Las Vegas and Hoboken, where Sinatra was born. New York and Las Vegas were among his favorite haunts.
The entertainer died 10 years ago.