Turnage was born in Corringham, Essex. His initial musical studies were with Oliver Knussen, John Lambert, and later with Gunther Schuller. He also has been strongly influenced by jazz, in particular by the work of Miles Davis.

In Autumn 2005, he was appointed the Royal College of Music's Research Fellow in Composition.

In 1990, Turnage was appointed the first Radcliffe Composer in Association with the City of Birmingham Symphony Orchestra. In 2006, Turnage was named a co-composer-in-residence of the Chicago Symphony Orchestra, a position he held alongside Argentinian composer Osvaldo Golijov.

In Autumn 2005, he was appointed the Royal College of Music's Research Fellow in Composition.​

Two elegies framing a shout (1997) 

"Speranza" Amal - Boston Symphony Orchestra - Daniel Harding 

Three Screaming Popes (After Francis Bacon For Large Orchestra)