All four of Schlossberg's grandparents were Russian Jews born near Poltava, Russia (now Ukraine), who arrived in the United States at Ellis Island.
He married Caroline Kennedy, the daughter of President John F. Kennedy and Jacqueline Kennedy Onassis, on July 19, 1986. They have three children:
- Rose Kennedy Schlossberg, born on June 25, 1988 in New York City, New York (named after Caroline's paternal grandmother Rose Kennedy)
- Tatiana Celia Kennedy Schlossberg, born on May 5, 1990 in New York City, New York (named after Edwin's former colleague, the lithographer Tatiana Grossman, and after Edwin's grandmother)
- John Bouvier Kennedy Schlossberg, born on January 19, 1993 in New York City, New York (named after Caroline's maternal grandfather, John Vernou Bouvier III (nickname Jack)).
He and Caroline Kennedy live on Park Avenue in Upper East Side, Manhattan.