Tucci was born on November 11, 1960, in Peekskill, New York, and grew up in nearby Katonah, New York. His parents, Joan (née Tropiano), a secretary and writer, and Stanley Tucci Sr. an art teacher at Horace Greeley High School in Chappaqua, New York, both of Italian descent, have distant roots in the town of Marzi in Calabria, Southern Italy. Tucci is the oldest of three children, including his sister, actress Christine Tucci. Screenwriter Joseph Tropiano is a cousin. During the early 1970s, he spent a year living in Florence, Italy.
He attended John Jay High School, in Lewisboro, New York, where he played on the soccer and baseball teams, although his main interest lay in the school's drama club, where he and fellow actor and high school friend Campbell Scott, son of actors George C. Scott and Colleen Dewhurst, gave well-received performances at many of John Jay's drama club productions. Tucci then attended State University of New York at Purchase, where he majored in acting and graduated in 1982. Among his classmates at SUNY Purchase was fellow acting student Ving Rhames. It was Tucci who gave Rhames, born Irving, the nickname "Ving".