Alexander Williams Randall was born in 1819 in Ames, New York, attending local schools and finishing his primary schooling at the Cherry Valley Academy. He then studied law with his father.

After moving with his family to Wisconsin Territory, Randall set up a law practice in Prairieville (later known as Waukesha), although it is not clear whether he ever earned a law degree. He then became involved in local politics, first as a Whig and ultimately as a Democrat. President James K. Polk named Randall as postmaster for Prairieville in 1845, and a year later, Randall served as a delegate to the state constitutional convention.

In 1848, now a Free Soiler Democrat, Randall began serving in the Wisconsin state legislature. His commitment to the antislavery movement brought him to the attention of the Republican Wisconsin governor, Coles Bashford, who, in 1855, tapped Randall to fill a vacant state court judgeship in Milwaukee.

Two years later, Randall was governor himself, serving until 1862, when he began considering an army career. President Abraham Lincoln convinced him otherwise and urged him to serve first as U.S. minister to the Holy See (the Vatican) in 1862 and then as first assistant postmaster general in 1863.

Under President Johnson, Randall became postmaster general, serving in the position from 1866 until 1869. Alexander Williams Randall died in 1872.