Faleomavaega was born in Vailoatai Village but grew up on the island of Oahu in Hawaii. He graduated from Kahuki High School and attended Brigham Young University-Hawaii, from which he earned an associated degree. He then transferred to Brigham Young University's main campus in Utah and earned a bachelor's degree in political science. Faleomavaega attended the University of Houston Law Center and the University of California, Berkeley, earning a Juris Doctor and a Master of Law degree. He served in the United States Army from 1966 to 1969, and as an officer in the United States Army Reserve from 1982 to 1989. Faleomavega served in the Vietnam War and left the military with the rank of captain. He and his wife are active members of The Church of Jesus Christ of Latter-day Saints.
Faleomavaega served as the administrative assistant to American Samoa Delegate A.U. Fuimaono from 1973 to 1975 and as staff counsel for the House Committee on Interior and Insular Affairs from 1975 to 1981. He worked as Deputy Attorney General for the territory of American Samoa between 1981 and 1984.
Faleomavaega entered elective politics when he ran along side A.P. Lutali in the 1985 gubenatorial race. He served as Lieutenant Governor of American Samoa from 1985 to 1989. Faleomavaega was elected as a Democrat to the House of Representatives, serving from January 3, 1989 to the present.
Faleomavaega appeared on the Colbert Report's "Better Know a Protectorate" segment on August 9, 2007. In 1987, he participated in an event that followed traditional Polynesian life experiences by sailing from Tahiti to Hawaii in a canoe .
As a delegate, Faleomavaega has worked to receive more federal funding for his home territory, particular for health care and other essential services. He has opposed free trade deals involving meats and seafood, as nearly one-third of his territory's population is involved in the tuna industry. He has proposed legislation that would allow residents of US territories to vote in presidential elections if they are active duty members of the military