If the ambassador is American, address him as "The Honorable (full name) Ambassador of the United States of America." If the ambassador is foreign, address him as "His Excellency (full name) Ambassador of (official name of the country)." These forms of address are valid for both envelope and letter labelling.
The form of address "The Honorable" is used exclusively when addressing American ambassadors as the form applies to persons appointed by the president of the United States. Informally, ambassadors and retired ambassadors can be addressed as Ambassador (last name). When outside the Western Hemisphere, American ambassadors should be addressed as "The Honorable (full name) American Ambassador."