Born in Trujillo Alto, Puerto Rico, Larrinaga studied at the Jesuit Seminario Conciliar of San Ildefonso in San Juan and at the Politechnic Institute in Troy, New York. In 1871 he received a degree in civil engineering from the University of Pennsylvania. After working in the United States, he returned to Puerto Rico and was named municipal architect for San Juan in 1872. He also was involved in many rural projects as well. Consequently, he was responsible for the construction or improvement of an aqueduct, roads, harbors, and the first railroad on the island. During the brief autonomist period, Larrinaga served as assistant secretary of the interior.
In 1899 Larrinaga helped found the Federal Party with Luis Muñoz Marín and then transferred his allegiance, as did many others, to the Unionist Party in 1904. He succeeded Degetau as Resident Commissioner to the United States Congress in 1904, a position he continued to hold until 1910. He also unsuccessfully tried to modify the Foraker Act and grant U.S. citizenship to Puerto Ricans. In 1906 he was selected to represent the United States to the Third Pan American Congress in Rio de Janeiro. In 1911, he returned to Puerto Rico where he continued his profession as civil engineer. From 1913 to 1917, he served on the executive council of Puerto Rico.
For additional information about Larrinaga, see the publication Hispanic Americans in Congress.