His likeness appears on a statue at the center of Logan Circle, Washington, D.C. He is also honored with a statue in Grant Park in Chicago, Illinois. He is the honoree of Logan County, Kansas; Logan County, Oklahoma; Logan County, Colorado; Logan County, North Dakota; and Logan Square, Chicago, which is the neighborhood chosen to mark Illinois' centennial. Logan is one of only three people mentioned by name in the Illinois state song. Upon his death, he lay in state in the United States Capitol rotunda. He is the father of U.S. Army officer and Medal of Honor recipient John Alexander Logan Jr. (1865–1899).