He discovered or co-discovered a number of comets, including periodic comets 11P/Tempel-Swift-LINEAR, 64P/Swift-Gehrels, and 109P/Swift-Tuttle (parent body of the Perseids meteor shower). He also discovered comets C/1877 G2, C/1878 N1, C/1879 M1, C/1881 J1, C/1881 W1, C/1892 E1, D/1895 Q1 (a.k.a. D/Swift, whose debris stream Mariner 4 probably encountered on September 15, 1967), C/1896 G1 and C/1899 E1, and co-discovered C/1883 D1 (Brooks-Swift). Note, however, comet 54P/de Vico-Swift-NEAT was discovered by his son Edward D. Swift rather than by him.
He discovered his last comet at the age of 79. He was one of the few people to see Comet Halley at two of its appearances, 76 years apart.
Apart from comets, he also discovered hundreds of nebulae.
His patron was the Rochester patent medicine businessman Hulbert Harrington Warner, who financed the building of an observatory for Swift. Warner went bankrupt in the Panic of 1893, which ended his financial support, and Swift then went to California to become director of Mount Lowe Observatory.
He was married twice, first to Lucretia Hunt in 1850 and then to Carrie D. Topping in 1864. Edward D. Swift was his son by the latter wife.