Varsi was born in Cagliari, Sardinia, and entered the Society of Jesus, an order of the Roman Catholic Church, on May 2, 1845.

He was educated at St. Teresa's College in Cagliari, and he went to Turin, Toulouse and Vals for advanced training in literature and philosophy.

In 1861, Varsi sailed to the United States and studied theology in Boston, Massachusetts, where he also taught physics and chemistry.

He moved to California in 1865 and took up a professorship in physics at Santa Clara College; two years thereafter he was assigned the presidency (1868–1876).

During his tenure, the original chapel was destroyed in an earthquake, and a large new theatre building, Exhibition Hall, replaced the old edifice.