The letter is dated 1919, when Hitler was a 30-year-old soldier, and 14 years before he became chancellor of Germany.
The letter has been known to scholars for some time. It is considered significant because it shows how early his anti-Semitic views were formed.
"He says, 'We don't want an emotional anti-Semitism, which leads to a street corner pogrom. What we need is a strong government, a government that will not be one of national impotence but that will be ruthless enough to remove the Jews altogether,'" said Rabbi Marvin Hier, founder and director of the Simon Wiesenthal Center Museum of Tolerance.
At the time, Hitler was serving in the German army, and had taken to riling up the troops with his anti-Semitic rants. A superior officer urged Hitler to put his ideas on paper.
Known as the Gemlich letter, the document was certified as authentic in 1988 by handwriting expert Charles Hamilton, who had revealed the infamous "Hitler Diaries" to be forgeries.
Adolf Gemlich created propaganda for the German army. Hitler wrote the letter to him at the suggestion of Captain Ulrich Mayr, to help popularize the notion that someone was responsible for Germany's defeat in World War I.
The L.A.-based Wiesenthal Center bought the letter from a dealer in historical documents for $150,000 last month.
It originally came from a U.S. Army soldier who found it in a Nazi archive near Nuremberg near the end of World War II.
The Associated Press contributed to this report.