Brewer was born in Addison Township and attended the rural schools and Romeo and Oxford Academies. He studied law, was admitted to the bar in 1864 and commenced practice in Pontiac. He was city attorney of Pontiac in 1866 and 1867 and circuit court commissioner for Oakland County 1866-1869. He was a member of the Michigan State Senate from the 20th District 1872-1874.

Brewer was elected as a Republican to the United States House of Representatives from Michigan's 6th District for the Forty-fifth and Forty-sixth Congresses, serving from March 4, 1877 to March 3, 1881. He was appointed consul general to Berlin on June 30, 1881, by U.S. President James A. Garfield and served from August 29, 1881, until June 7, 1885. He was again elected to the U.S. House for the Fiftieth and Fifty-first Congresses, serving from March 4, 1887 to March 3, 1891. He declined to be a candidate for renomination in 1890 and resumed the practice of law in Pontiac. He was a delegate to the Republican National Convention in 1896 and was appointed a member of the United States Civil Service Commission by President William McKinley January 18, 1898, and served until his death in Washington, D.C.. He is interred in Oak Hill Cemetery, in Pontiac, Michigan.