The son of Henry F. Suessdorf, he was born in Valdez, Alaska, United States, where his father operated from 1907 to 1917 the Copper Block Buffet, a hotel and saloon that offered electric lights, hot baths and steam, and served men only.
At the time of the 1940 U.S. Census (April 1940), the couple was renting a small house in Hollywood; his occupation was listed as a "salesman" working in a gasoline station.
Suessdorf was best known for his collaboration with lyricist John Blackburn in composing the jazz standard, "Moonlight in Vermont", which was first recorded in 1944 by Billy Butterfield's Orchestra featuring Margaret Whiting.
Suessdorf composed "Christmas Madonna" (1958) and "Coral Sea" (1965) with lyrics by Nick Cea; "Key Largo" (1948) (sung by Marian McPartland) and "She Doesn't Laugh Like You" (1964) with Benny Carter and Leah Worth; and a 1949 hit for Perry Como, "Did Anyone Ever Tell You, Mrs.
Apart from the many other performers who have recorded Suessdorf's compositions, including Billie Holiday and Frank Sinatra, Sarah Vaughan's compilation album Music of the Stars, Volume 2: Songs Recorded by Sarah Vaughan included both "Key Largo" and "Moonlight in Vermont".