Samuel Prowse Warren was born in Montreal, Quebec, on February 18, 1841, the son of organ builder Samuel Russell Warren (1809-1882). Two of Samuel P. Warren’s uncles and a brother were also organ builders. At the age of 12, Warren gave his first organ recital at St. Stephen's Chapel in Quebec; his musical ability was such that he soon succeeded his father as organist at the city's American Presbyterian Church. As would become his pattern, Warren stayed in that position for an extended period--in this case eight years. In 1861, at 20, he went to Berlin to study organ and theory with Karl August Haupt, piano with Gustav Schumann, and instrumentation with Wilhelm Wieprecht.

After returning to Montreal in 1865, Warren moved to New York City, where he gave his first public recital in January 1866. Later that year he was appointed organist of All Souls Unitarian Church, a position he held until April 1868. He played at Grace Church (Broadway and 10th Street) from 1868 to 1874, returning there in 1876 after two years as organist at Holy Trinity Episcopal Church between 1874 and 1876. Warren then remained at Grace Church as organist and choirmaster until 1894. While at Grace Church, Warren took an active part in the musical life of New York City, especially in the realm of organ and sacred and secular vocal music. He established a weekly series of organ recitals, giving over 230 recitals at Grace Church alone, and was organist for Leopold Damrosch's Oratorio Society from 1874 to 1879. Warren also conducted the New York Vocal Union from 1880-1888.

In 1895, Warren accepted a position as organist at the First Presbyterian Church in Orange, New Jersey, a position he held until his death. One year later he participated in the founding of the American Guild of Organists, serving as its honorary president from 1902 to 1908. In addition to performing, Warren composed music for organ and piano, including service and choral works. He also transcribed orchestral music for the organ, namely works by Beethoven, Wagner, and Mozart. Gustav Schirmer regularly invited him to edit compositions for publication. Warren taught many prominent organists of his day, including William Crane Carl, W. C. Hammond, William C. Macfarlane, Gerrit Smith, and Frederick T. Steinway. He championed women organists and taught Harriette Judd (the first organist and choir director at Madison Avenue Presbyterian Church) and Augusta Lowell (organist at the Church of the Incarnation). Between 1902 and 1908, Warren also acted as a musical examiner for the American Guild of Organists and Toronto College of Music.

Warren married twice: to Emily Augusta Millard (1843-1901) on January 16, 1867 in Montreal, Quebec, and to Jeanne Josephine Coker (an opera singer) on July 8, 1909 in Poughkeepsie, New York. He died in New York City on October 7, 1915.