Robert W. Brady was born in Hancock, Maryland on October 6, 1825. He studied at St. John's College, MD and entered the Society of Jesus on August 31, 1843 at Frederick, MD. In 1845, Brady became a professor of rudiments at Georgetown College. Brady’s superiors transferred him in 1847 to the newly founded College of the Holy Cross in Worcester, Massachusetts. Brady was ordained a priest by Archbishop Peter Richard Kenrick of St. Louis on July 25, 1857. In 1860 he was sent to Loyola College in Baltimore, where he became a minister and teacher of algebra. On July 10, 1863 Brady was elected to a three-year term as the treasurer and a member of the board of directors of Boston College.
On February 27, 1867, Brady was named the president of the College of the Holy Cross. Brady left this role to become the second president of Boston College on August 27, 1869. On June 28, 1883, he again returned to the College of the Holy Cross to begin his second presidency. Brady's second term as president of Holy Cross ended on August 2, 1887. On March 26, 1891, Brady died of pneumonia in Washington D.C., aged 65.