He attended Thomas Baker’s Academy in Colerain Township.
During the American Civil War, he enlisted as a private in Company K, Ninety-seventh Regiment, Pennsylvania Volunteers, in October 1861, for three years, and reenlisted May 1864. He was honorably discharged in December 1864. On February 28, 1865, was commissioned a second lieutenant for bravery on the field of battle.
After the war he attended the State Normal School at Millersville, Pennsylvania, and the law department of the University of Michigan at Ann Arbor.
He was admitted to the bar in 1868 and commenced practice in Lancaster, Pennsylvania. Brosius was elected as a Republican to the Fifty-first and to the six succeeding Congresses.
He was chairman of the United States House Committee on Reform in the Civil Service during the Fifty-fourth and Fifty-fifth Congresses, and of the United States House Committee on Banking and Currency during the Fifty-sixth Congress. He served until his death in Lancaster in 1901.
Interment in Greenwood Cemetery.