Morton was born in Louisville, the son of David Clark Morton, a physician, and his wife, Mary Harris Ballard Morton, an heiress to a flour milling business. He was related to George Rogers Clark, a military officer who served during the American Revolutionary War. Morton was one of three children; his brother Thruston B. Morton also had a career in politics, serving as chairman of the Republican National Committee and representing Kentucky in both the United States House of Representatives and then the United States Senate.  Morton received his early education from the Woodberry Forest School near Orange, Virginia, and in 1937 graduated from Yale University, where he was a brother of the Delta Kappa Epsilon fraternity (Phi chapter). Like his father, Morton worked to become a physician and entered the Columbia University College of Physicians and Surgeons. However, he dropped out after only one year. In 1939, Morton married the former Anne Jones. They had two children, David Clark and Anne Morton.  In 1938, Morton was commissioned in the United States Navy but only served for a short time due to problems with his back. Afterwards, he entered his family's flour business, Ballard & Ballard. In 1941, at the outset of World War II, Morton enlisted in the Armored Field Artillery of the United States Army as a private and served in the European Theater. He received a commission during the war and left the army as a captain in 1945.  After the war, Morton returned to the family business, where he served as president from 1947 to 1951. In 1952, the business was merged into the Pillsbury Flour Company, where Morton went on to serve as a director and a member of the executive committee for several more years.

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