Rosenblum joined the Associated Press at Newark in 1965. His international career began in 1967, when the AP sent him to cover mercenary wars in Congo. Since then Rosenblum has run AP bureaus in Kinshasa, Lagos, Kuala Lumpur, Jakarta, Singapore, Buenos Aires, and Paris. From 1979 to 1981 he was editor of the International Herald Tribune but later returned to AP as special correspondent, based in Paris.

Rosenblum left AP in 2004, and in 2008, launched dispatches, a quarterly magazine with co-editor Gary Knight and publisher Dr. Simba Gill. Additionally, Rosenblum is a professor of journalism at the University of Arizona, Tucson, where he teaches International Reporting.

Rosenblum won an Overseas Press Club Award in 1989 and has been nominated for eight Pulitzer Prizes. Additionally, he won AP's top reporting award in 1990, 2000 and 2001.