Browne attended Cooper Union and got his start at the New York Journal American as a copy boy and later worked in the art department. He joined the army, producing work for the engineering unit and created Jinny Jeep, a comic strip about the Women's Army Corps.
In 1954, Browne and cartoonist Mort Walker co-created the comic strip Hi and Lois, a spin-off of Walker's popular Beetle Bailey strip, featuring Beetle's sister, brother-in-law and their family. Walker wrote the strip, which Browne illustrated until his death. The series is now drawn by his son Chance and written by Walker's sons. In 1973, Browne created Hägar the Horrible about an ill-mannered red-bearded medieval viking. The comic is now produced by his son Chris. Both strips have been successful, appearing in hundreds of newspapers for decades.
Browne died of cancer on June 4, 1989, in Sarasota, Florida.
Browne was recognized for his work by the National Cartoonists Society with their Humor Comics Strip Award in 1959, 1960, 1972 and 1977 for Hi and Lois, and again in 1984 and 1986 for Hägar the Horrible. He received their Reuben Award for Hi and Lois in 1962 and for Hägar the Horrible in 1973. That same year the NCS honored him with their Elzie Segar Award.