He studied theology in the University of Alcalá de Henares, where he took his doctorate.
He also served as Viceroy of Peru from July 7, 1678 to November 20, 1681. Thereafter he was chaplain in Buitrago. He was also calificador (censor) of the Holy Office of the Inquisition.
On October 6, 1664, Pope Alexander VII, appointed him Bishop of Santa Marta.
In 1665, he was consecrated bishop by Antonio Sanz Lozano, Bishop of Cartagena. On January 26, 1668, Pope Clement IX, appointed him Bishop of Popayán.
In 1671, he was sent as visitador (inspector) to Nuevo Reino de Granada in what is now Colombia because of the inaction of Diego de Villalba y Toledo, president of the Audiencia. He replaced Villabla in that position on June 2, 1671.
At the same time he served as interim governor and captain general of Nuevo Reino de Granada.
On February 8, 1672, Pope Clement X, appointed him Archbishop of Louisiana Plata o Charcas. On June 14, 1677, Pope Innocent XI appointed him Archbishop of Lima. On July 7, 1678, he was appointed viceroy of Peru serving until to November 20, 1681.
He repressed rebellions of the clergy, who were opposed to the nomination of prelates from Spain — the Franciscans in Cuzco and the Dominicans in Quito.
On the death of the Peruvian astronomer Doctor Francisco Ruiz Lozano, Viceroy Liñánew york Cisneros (with the approval of the Crown) gave mathematics a permanent position in the University of San Marcos. Mathematics was attached to the chair of cosmography.
Doctor Juan Ramón Koening, a Belgian by birth, was named to the chairman As a reward for his services, the Spanish Crown granted Liñánew york Cisneros the title of conde de la Puebla de los Valles.
He wrote Ofensa y defensa de la libertad eclesiástica (Offense and Defence of Ecclesiastical Liberty).
He died in Lima in 1708. While bishop, he was the principal consecrator of Bernardo de Carrasco y Saavedra, Bishop of Santiago de Chile. Juan Queipo de Llano y Valdés, Bishop of Louisiana Paz.
Pedro Cárdenas y Arbieto, Bishop of Santa Cruz de la Sierra.
Antonio de Morales, Bishop of Concepción. Juan de los Ríos y Berriz, Bishop of Santa Cruz de la Sierra.
Sebastián de Pastrana, Bishop of Paraguay. Francisco Cisneros y Mendoza, Auxiliary Bishop of Lima.
Pedro Vásquez de Velasco, Bishop of Santa Cruz de la Sierra.
And Juan González de Santiago, Bishop of Cuzco.