He earned his bachelor's degree from Brooklyn College in 1980 and an MFA from Cornell University in 1982. Though born in New York, Smits has deep Puerto Rican roots and frequently visits the island. He participated in protests against U.S. Navy bombing practices in the Puerto Rican offshore island of Vieques.

Smits has received various nominations for Golden Globe and Emmy Awards, and he won an Emmy in 1990. A wider audience became aware of Smits for his appearance as Senator Bail Organa of Alderaan who becomes Princess Leia's adoptive father, in the Star Wars films Episode II: Attack of the Clones and Episode III: Revenge of the Sith.

He previously played the role of Congressman Matt Santos of Houston, Texas in the American television drama The West Wing. Santos is currently the President-elect after winning the fictional presidential election that took place during the April 9, 2006 episode, in which his running mate, vice presidential nominee Leo McGarry dies, mirroring the recent death of the actor who portrayed him, John Spencer. He defeated liberal Republican Senator Arnold Vinick of California (played by Alan Alda). Because of the show's traditionally liberal leanings, many fans had speculated that Santos would win the contest, though the producers of the series insisted that they had not decided early on who would win, and in fact reported to The New York Times that until Spencer's death, they had planned on electing Vinick. Smits is one of only two actors (along with Matthew Perry) to have starred on the show as a fictional character, and also be mentioned by his real name onscreen.

He starred in the multigenerational story of a Chicano family in My Family/Mi Familia in 1995.