Estigarribia was of humble origin, son of a peasant and silversmith, Matthew Estigarribia, and Casilda Insaurralde. Born in San Roque rural town of Santa Elena, Department of Cordillera, Paraguay. Elementary school was made in his hometown and in 1888 went to study at Trinity College of Agriculture, a college of agriculture. However, after obtaining his diploma, Estigarribia switched careers and in 1910 joined the army with the rank of Lieutenant of Infantry.
Educated as an agronomist, he joined the national Army in 1910 and spent time in Chile and in Saint Cyr's military academy in France for additional training. He commanded the First Infantry division during the Chaco War and was promoted successively to brigadier, division general, and commander-in-chief of the armed forces. In 1935, he made a victorious return to Asunción as "Hero of the Chaco War" and was awarded a lifetime pension of 1,000 gold pesos a month. He was dismissed from the position of armed forces chief after President Eusebio Ayala was overthrown in the Febrerista revolution by Rafael Franco, but served as Paraguay's ambassador to the United States.
He completed courses in Chile, from 1911 to 1913, the Military School of Bernardo O'Higgins . In 1917 he was promoted to captain. Played an important role in the revolution of 1922 in Paraguay and was later promoted to Major. For their skills was selected to attend the course staff, three-year at the École Supérieure de Guerre (Paris, France) where he was a disciple of General Maurice Gamelin and Marshal Foch, where he graduated with top notes. On his return in 1928 was appointed Chief of Staff of the Army. Less than a year after being named was removed from office because of disagreements with the government regarding the strategy for defending the Chaco, "The Chaco should be advocated abandoning it," he argued, that is, the point was not occupy the land but to destroy the enemy. However, as the war against Bolivia seemed inevitable, the government decided that Lieutenant Colonel Estigarribia was the man who was needed in the Chaco. He was then 44 years. Small of stature, so peaceful, introspective, or his personality or his austere uniform of campaign-whose sleeves were invariably short-set him apart from the rest of the officers.
The definition of the Chaco War would be a war of "communications", where the handling of space and time would be essential, determined that the Paraguayan government to accept its general mobilization plan and the beginning of the first offensive surprise Paraguay (September- December 1932) before Bolivia could mobilize their resources.
Given clear that the army under his command was all that Paraguay with maximum effort could have led a successful military campaign against successive Bolivian army, superior in men and materials, making back to the Rio Parapiti. His strategic thinking about the war of movement, the importance of logistics (especially water), concentration of forces surprise, the passage from the defensive to the offensive and thorough knowledge of the enemy and terrain of operations placed him in a privileged among military drivers between the two world wars. Made the most of the officers under his command and combative and moral virtues of Paraguayan soldier. He directed the Paraguayan army during the first year of war with the rank of colonel. He was promoted to general after the victory of Campo Grande and Pozo Favorite. In recognition of services rendered to the defense of the Chaco was promoted to the rank of marshal after his death in 1940.
Estigarribia was elected President for a four-year term in 1939, assuming office on August 15. Six months later on February 19, 1940, Estigarriba dissolved the legislature and suspended the Constitution. Declaring that "our nation is on the edge of horrible anarchy," he announced that democracy would be restored as soon as a workable constitutional framework could be designed. It turned out to be an empty promise; within five months, he recast the constitution into a severely authoritarian document that granted sweeping powers to the president.
On September 7, 1940, Estigarriba and his wife were on a tour of the Paraguayan interior. On a trip from Altos to his country residence in San Bernardinos, his plane crashed in Agapuey and all on board were killed. Estigarribia was succeeded by Higinio Morínigo and posthumously promoted to the rank of marshal. His authoritarian constitution would remain in effect until 1967.