Rosenberg was born and raised in Passaic, New Jersey. Alan's late brother, Mark, was a political activist in the 1960's, later a film producer; while his first cousin is musician Donald Fagen.

Alan's German Jewish parents gave him enough money to apply to graduate school, but while studying at Case Western Reserve University he found another passion and became New York state's backgammon champion in 1982. On graduating in 1972, he had gambled most of his parents money away, and could only afford one application to Yale School of Drama. Rosenberg dropped out halfway through his second year, after his heart was broken by classmate Meryl Streep.

Rosenberg is perhaps best known for his character Eli Levinson which appeared in both the series Civil Wars and the popular L.A. Law. He is also well known for his character Ira Woodbine in the sitcom, Cybill. More recently he was seen in the legal drama The Guardian as "Alvin Masterson".

In 1995, he received an Emmy Award nomination for a guest-starring role in the hit drama ER.

He was elected the 24th president of Screen Actors Guild (SAG) on September 23 2005. Rosenberg succeeds Melissa Gilbert, who served as president since 2001 and chose not to run for a third two-year term. Rosenberg received 39.99 percent (10,748 total votes) of the nationwide vote of the Guild’s general membership, defeating Morgan Fairchild and Robert Conrad. Fairchild received 34.72 percent (9,332 total votes) and Conrad received 25.29% percent (6,797 total votes). Rosenberg formally assumed the office of Guild president on September 25, and will serve a two-year term.

In 2005 he appeared as shady defense attorney "Adam Novak" in an episode of CSI: Crime Scene Investigation co-starring alongside his real life wife Marg Helgenberger. Novak was portrayed as a womanizer who encountered Catherine (Helgenberger) in a bar and later became the prime suspect in two homicides. His character appeared once again in the 2007 episode Leaving Las Vegas as a lawyer defending a client who turned out to be guilty of two separate crimes, and yet the evidence failed to pin him down, resulting to a not guilty verdict which annoyed Catherine so much that she began to undergo further investigation.

In 2007 he started hosting a Public Television program, "Life: Part 2", produced in St. Paul, Minnesota. He moderates panel discussions about issues that baby boomers face as they age.

Originally married to actress Robin Bartlett, Rosenberg met Marg Helgenberger in New York while guest-starring on her soap "Ryan's Hope." The two conversed for hours between shots on the motel-room set.

Four years later, the newly divorced Rosenberg walked into a West Hollywood bank and spotted Helgenberger in line - they exchanged telephone numbers. Within two months the actors were living together, and eloped in 1989 to avoid upsetting a Jewish relative. Their son, Hugh, was born the following year.