Born in Milo in Ashley County in south Arkansas, Norrell attended the public schools, the University of Arkansas at Monticello, then known as Arkansas Agricultural and Mechanical College, the University of the Ozarks, then College of the Ozarks in Clarksville, Arkansas, and the University of Arkansas at Little Rock Law School.
Upon his death, he was succeeded in Congress by his widow, Catherine Dorris Norrell. During World War I, Norrell served in the Quartermaster Corps of the United States Army. In 1920, he was admitted to the bar and commenced practice in Monticello in Drew County, Arkansas.
He was the Senate President from 1934 to 1938 under Lieutenant Governors William Lee Cazort and Robert L. Bailey.
Norrell was elected as a Democrat to the Seventy-sixth and to the eleven succeeding Congresses and served from January 3, 1939, until his death in Washington, District of Columbia
From 1930 to 1938, Norrell served as member of the Arkansas State Senate.
