On May 18, 1880, he married Susan Bonaparte Palmer, daughter of Brigadier General Innis N. Palmer, and they had five children. Their son, Innis P. Swift also became a major general. One of their daughters, Clara, was the wife of Brigadier General Evan Harris Humphrey.
Swift was initially assigned to the 14th Infantry, and soon transferred to the 5th Cavalry. He spent several years at posts in the western United States during the American Indian Wars, including assignments in Wyoming, Montana, Nebraska, Idaho, and Colorado. From 1887 to 1890 he was aide-de-camp to Wesley Merritt.
He took part in the Spanish–American War, serving in Cuba and Puerto Rico with several volunteer units from Illinois, and advancing from temporary Major to temporary Colonel and commander of the 4th Illinois Volunteer Infantry by the time he returned to the regular Army in 1899.
His early 1900s assignments director of the Army War College and military observer in Manchuria of the Russo-Japanese War. He commanded the 2nd Cavalry Division on the U.S.-Mexico border during the Pancho Villa Expedition.
Swift later served as head of the U.S. Military Mission and commander of U.S. forces in Italy and was promoted to major general. He reached the statutory retirement age of 64 on May 11, 1918, but continued to serve until September. Swift was awarded the Order of Saints Maurice and Lazarus (Commander) for his service in Italy.
In 1919 and 1920 he was recalled to temporary duty as a lecturer on tactics for Reserve Officer Training Corps units at several colleges and universities.