Swift was born in Cincinnati, Ohio to Samuel W. Swift and Elizabeth Swift (born Bell). His family moved to Galena, Illinois when he was young. By his teenage years, the family was living in Chicago. Prior to serving as mayor of Chicago, Swift served two terms as an alderman. From 1887 to 1889, he was the city's Commissioner of Public Works. Swift died on July 2, 1912 in Chicago, Illinois from a heart attack, aged 66.