Cooper was born in New York City, the younger son of the writer Wyatt Emory Cooper and the artist, fashion designer, writer, and heiress Gloria Vanderbilt. His maternal grandparents were millionaire equestrian Reginald Claypoole Vanderbilt and socialite Gloria Morgan Vanderbilt, and his maternal great-great-great-grandfather was business magnate Cornelius Vanderbilt, of the prominent Vanderbilt shipping and railroad fortune. He is also a descendant, through his mother, of Civil War brevet Major General Hugh Judson Kilpatrick, who was with General William T. Sherman on his march through Georgia. Through his "Vanderbilt" line, he is a second cousin, once removed, of screenwriter James Vanderbilt.

Cooper's father suffered a series of heart attacks while undergoing open-heart surgery, and died January 5, 1978, at the age of 50. Cooper considers his father's book Families to be "sort of a guide on...how he would have wanted me to live my life and the choices he would have wanted me to make. And so I feel very connected to him."

Cooper's older brother, Carter Vanderbilt Cooper, committed suicide on July 22, 1988, at age 23, by jumping from the 14th-floor terrace of Vanderbilt's New York City penthouse apartment. Anderson cites Carter's suicide for sparking his interest in journalism.

Cooper is openly gay; according to The New York Times, he is "the most prominent openly gay journalist on American television." For years, Cooper avoided discussing his private life in interviews. On July 2, 2012, however, he gave Andrew Sullivan permission to publish an email that stated, in part:

I've begun to consider whether the unintended outcomes of maintaining my privacy outweigh personal and professional principle. It's become clear to me that by remaining silent on certain aspects of my personal life for so long, I have given some the mistaken impression that I am trying to hide something—something that makes me uncomfortable, ashamed or even afraid. This is distressing because it is simply not true. ... The fact is, I'm gay, always have been, always will be, and I couldn't be any more happy, comfortable with myself, and proud.

Cooper and his boyfriend, gay bar owner Benjamin Maisani, have been dating since 2009. Cooper considered coming out to the public when same-sex marriage became legal in New York in July 2011. In 2014, the couple purchased the Rye House, a historic estate in Connecticut. Tim Cook, of Apple, turned to Cooper for advice before he subsequently made the decision to publicly come out as gay.