Born in Zizonys, Biržai district municipality, in 1882, Galvanauskas completed his secondary education at the Gymnasium of Jelgava, Latvia in 1902. He then took up studies in engineering in St. Petersburg, Russia. He was active in the Russian Revolution of 1905 in Lithuania, and founded the Lithuanian Peasants' Union. Later he was elected as a delegate to the Great Seimas of Vilnius. He was arrested and imprisoned in the Panevėžys Prison, but escaped and with the help of Felicija Bortkevičienė fled abroad.
Between 1906 and 1919, he lived first in Finland, then in Liège (Belgium) from 1908, where he completed his studies and received a diploma in mining engineering from the Technical University and another one from the Electrotechnical Institute, then he worked on the railroad in Serbia. In 1919, he was a member of the Lithuanian delegation at the Versailles Conference being held in Paris. In October 1919, Galvanauskas became Prime Minister of Lithuania, serving until April 1920. During that time he also served as Minister of Finance, Trade, and Industry. In 1921 Galvanauskas was also a delegate to the League of Nations, where he worked to obtain international recognition of Lithuania.
Between February 1922 and June 1924, Galvanauskas was Lithuania's Minister of Foreign Affairs. During this period, Galvanauskas' efforts also helped to establish the University of Lithuania in 1923. His home was the target of a bomb attack by extreme nationalists (Committee for the Salvation of Lithuania) who suspected him and his French wife to be pro-Polish, he was injured.