A prominent Democrat even as Vermont was trending towards the Republicans, Phelps was the son of Senator Samuel S. Phelps and his first wife, Frances (Shurtleff) Phelps. Edward Phelps graduated from Middlebury College in 1840, taught school in Virginia, and studied for a career as an attorney, first at Yale Law School, and then in the office of Middlebury attorney Horatio Seymour. He practiced in Burlington, and served as Second Comptroller of the Treasury from 1851 to 1853. He supported the Union, but as a critic of what he regarded as the excesses of the Abraham Lincoln administration. He served as a delegate to the Vermont constitutional convention of 1870, and was one of the founders of the American Bar Association. Phelps served as ABA president from 1880 to 1881. In 1880, he was the unsuccessful Democratic nominee for Governor of Vermont.