Abbe was born in New York City and educated there at City College; he later taught at the University of Michigan. He then spent two years (1864–66) in Russia at the Pulkovo Observatory under Otto Struve. On his return to America he worked as director of the Cincinnati Observatory (1868–70).
Abbe was the first official weather forecaster in America. He was appointed, in 1871, chief meteorologist with the weather service, which was later formed into the US Weather Bureau (1891), and remained in this organization for the rest of his life. He was one of the first scientists to see the revolutionary role the telegraph had to play in weather forecasting and used reports conveyed to him from all over the country.