Peter was a Belgian born on February 8, 1795 in Sichern near Diest in the Diocese of Mechlin. He was 20 years old when he entered the seminary at Mechlin, but eight months after his ordination he decided to become a Jesuit. On October 29, 1819, at the age of 24, he entered the Society at Hildesheim. He became the chaplain and confessor of Duke Ferdinand d'Anhalt-Koethen and after the death of the Duke he rendered the same service for the Duchess when she moved to Vienna. In 1850 he became Rector of Louvain and professor of Canon Law. Then, two years later, he became the Provincial of Austria.

European politics at that time were in a sorry state and governments shifted from monarchy to republic overnight. It was a time of political unrest and there seemed to be a revolution going on somewhere at any given time. In Italy, too, the reunification was taking place with no one really knowing what it meant or how it would be accomplished.

At the establishment of the Republic in 1873 the Jesuits were expelled from the Collegio Romano losing title to the name as well as to the property. They moved into the German College on via del Seminario, changed its name to Université Gregoriana del Collegio Romano, and remained in that location until the political situation had changed in 1930 when they moved into their new building near the Quirinale.

In 1873, too, it was judged prudent to move the Curia. On October 30, 1873 the General and two Fathers moved to the Villa San Girolomo in Fiesole, which, then, became the seat of the Jesuit Curia Generalis. The air was certainly better there than in Rome both physically and politically.

On May 11, 1883 Father Beckx announced that he was convening the 23rd General Congregation for September 15. The reason for this announcement was that, with the Holy Father's consent, he had selected Father Antonio Maria Anderledy as his permanent Vicar General with the right of succession. He wanted the approval of the General Congregation for this decision. Beckx was getting feeble and needed the help of a trusted lieutenant. The Fathers of the Congregation approved his plan of action after Leo XIII asked Beckx to remain and give guidance. On September 24, 1883, Beckx then imposed silence on the whole Congregation in reference to this affair.

Beckx had been General for 33 years and 8 months, from 1853 until 1887, when he died at age 88 years in Rome on March 4, 1887. He was succeeded as superior general by Anton Anderledy (1887-1892).