Born in Klagenfurt, Austria, Nucci was raised in Italy until the age of seven, when his family relocated to the United States. His father, a textile machinery seller, was from Italy. He has two sisters, Natalie and Elle. After temporarily living in Queens, New York, the family settled in California's San Fernando Valley, where Nucci graduated from Grant High School. He married Paula Marchall in 2003, and has two daughters. Marshall and Nucci played lovers in the 1997 Bette Midler film That Old Feeling.
Nucci played characters who were unceremoniously killed off in short succession during three different 1990s blockbuster action films —Eraser, The Rock and Titanic — three of which were released within twenty months of one another in 1996 and 1997. His character did manage to survive in the 1993 film Alive: The Miracle of the Andes.
Nucci played Gabriel Ortega on the CBS soap opera Falcon Crest from 1988 to 1989, as Vincent Sforza, alongside Marguerite Moreau, inFirestarter 2: Rekindled, as Petty Officer Danny Rivetti in the 1995 Gene Hackman-Denzel Washington submarine thriller Crimson Tide, and as Spider Bomboni in Book of Love. He took the roles of Benny Rodriguez in the straight-to-video film The Sandlot: Heading Home and a Port Authority police officer in the 2006 film World Trade Center. He also played Jack Dawson's Italian friend, Fabrizio De Rossi, in the 1997 blockbuster film Titanic.
Notable television appearances include Growing Pains, Out of This World, Quantum Leap, Family Ties, The Twilight Zone, Snoops, Just Shoot Me, House, M.D., Without a Trace, Criminal Minds, The Mentalist, CSI: NY and two episodes of Castle. Along with Ernie Hudson, Nucci co-starred in the short-lived police drama series 10-8: Officers on Duty.
In 2009, he portrayed John Gotti in Sinatra Club. In 2010, he starred as Dante McDermott in the science fiction filmNephilim. In 2011, he co-starred in the feature Escapee.