Greene was born to middle class parents in Brooklyn. Both his parents were actors. His father, who was born in Harlem, was a union organizer, one of the first African Americans elected as an officer in the Screen Actors Guild, and belonged to the Harlem Renaissance movement. Greene's father was blacklisted as a Communist in the 1950s and forced to take uncredited parts in movies. Greene's parents gave him his first camera when he was eleven years old. Greene began his art career as a painter, but started taking photos as a means of cataloging material for his paintings. In 1971, when Greene was a member of the anti-war movement and the Black Panthers, his friend, photographer W. Eugene Smith offered him space in his studio and encouraged him to study photography at the School of Visual Arts in New York and the San Francisco Art Institute. Greene held various jobs as a photographer, including taking pictures of rock bands and working at Newsday. In 1986, he shot fashion in Paris. He called himself a "dilettante, sitting in cafes, taking pictures of girls and doing heroin". After a friend died of AIDS, Greene kicked his drug habit and began to seriously pursue a photography career. He began photojournalism in 1989, when his image ("Kisses to All, Berlin Wall") of a tutu-clad girl with a champagne bottle became a symbol of the fall of the Berlin Wall. While working for the Paris-based photo agency Agence Vu in October 1993, Greene was trapped and almost killed in the White House in Moscow during a coup attempt against President Boris Yeltsin. He has covered the war-torn countries Azerbaijan, Georgia, Iraq, Somalia, Croatia, Kashmir, and Lebanon. He has taken pictures of the genocide in Rwanda in 1994 and the US Gulf Coast in the aftermath of Hurricane Katrina in 2005. Since 1994, Greene is best known for his documentation of the conflict in Chechnya, between rebels and the Russian armed forces, which was compiled in his 2004 book, Open Wound. These photos have drawn attention to the "suffering that has marked the latest surge in Chechnya's centuries-long struggle for independence from Russia". In 2008, Greene revealed that he had hepatitis C, which he believed he had contracted from a contaminated razor while working in Chad in 2007. After controlling the disease with medication, he traveled to Afghanistan and shot a story about "the crisis of drug abuse and infectious disease". Greene has lived and worked in Paris since 1986.
He said: “My wife has left me but instead of becoming an alcoholic, I would go and shoot war”.