Born in Philadelphia, as an amateur landscape painter, Haseltine studied at the University of Pennsylvania and then at Harvard University, where he received a degree in 1854. He first exhibited his paintings at the Pennsylvania Academy of Fine Arts, after which he sailed to Europe, who were studying in DÃ¼sseldorf, then traveling up the Rhine into Switzerland and Italy. In late 1857 he settled in Rome, and in the following months made numerous excursions to draw the landscape around Rome and on Capri.
In 1858 Haseltine returned to Philadelphia, then in Tenth Street Studio Building in New York City, then a central point for American landscape painters; also in the building were Frederic Edwin Church, Albert Bierstadt, and Worthington Whittredge. Though many of his paintings from this time derived from his European sketches. The precision with which he painted these landscapes won critical praise, and Haseltine was elected an Associate of the National Academy of Design in 1860, and a full Academician in 1861.
In 1864 Haseltine's wife died in childbirth. He spent some time training his nephew, Howard Russell Butler, but he moved after he married Helen Marshall in 1866. Initially the family considered settling in Paris, but in 1867 they moved to Rome, which would for most of Haseltine's subsequent years serve as his home and point of departure from which to produce views of the European landscape. Haseltine also traveled and drew in France, Holland, Belgium, and the Netherlands, summering in Bavaria and the Tyrol in the 1880s and 1890s. In his later years he also returned periodically to the United States, making a final trip to the west in 1899.
Haseltine died of pneumonia in Rome in 1900. He is buried at the American cemetery right next to Episcopalian Church, of which he was one of the founding members.