Orlando Cole was born in Philadelphia in 1908 and celebrated his hundredth birthday in August 2008. His father was a violinist who played in the Philadelphia Orchestra. At seven he started the piano and at twelve took up percussion. When he got to West Philadelphia High School there were no vacancies for these instruments in the orchestra, so—distinctly late—he took up the cello.

His teacher at the Curtis Institute was the English cellist and influential teacher Felix Salmond (1888–1952), who was head of the cello department from 1925 to 1942. Salmond had played in the premieres of Elgar's String Quartet and Piano Quintet, was soloist in the Cello Concerto conducted by the composer in 1919, and moved to the United States in 1922. He played Barber's Cello Sonata, sometimes with the composer, after Cole gave the premiere in 1932. Cole made his New York debut while still a student in 1929 and served as Salmond's assistant after he was appointed to the Curtis faculty in 1938.

Cole taught at Curtis for seventy-five years, and his pupils included many of the world's finest cellists. He was a founder-member of the Curtis Quartet, performing with them until 1980; three of the members were together for fifty years. The quartet gave a series of concerts in London to mark King George V's Silver Jubilee in 1935 and played for President and Mrs. Roosevelt at the White House. The group returned to Europe in 1936 and 1937 and would have gone back in 1938 but realized it was no time to travel there because of the Hitler menace. They gave the American premiere of Barber's String Quartet in 1937. In 1943 Cole founded the New School of Music in Philadelphia, now affiliated with Temple University. He gave master classes throughout the United States, Europe, and the Far East.

In 1986 Cole received an honorary doctorate from the Curtis Institute; in 1990 the American String Teachers Association named him Teacher of the Year; and in 2000 Curtis gave him its first-ever Alumni Award.

As a student at Curtis, Cole remembered hearing Menotti working on his first opera Amelia Goes to the Ball, so the overture was included in a tribute concert to Cole held at Curtis on October 19, 2005.