Gibbs was born in New York, the daughter of Janet (née Stang), who worked at Friends Seminary, and Howard Glenn Gibbs, who was the associate national director for the Boys Clubs of America. She graduated from Yale University in 1982, summa cum laude, with honors in history. She studied at New College, Oxford as a Marshall Scholar (M.A. in Politics, Philosophy and Economics).
She joined TIME in 1985 as a part-time fact checker in the International section. She became a writer in 1988 and has written more than 100 cover stories, including the black-bordered special issue on the September 11 attacks, which won a National Magazine Award in 2002. The Chicago Tribune named her one of the ten best magazine writers in the country in 2003; her articles are included in the Princeton Anthology of Writing, Best American Crime Writing 2004, Best American Political Writing 2005 and TIME: 85 years of Great Writing. She has been a frequent guest on radio and television talk shows, including the Today Show, Good Morning America, Charlie Rose, and a guest essayist on the NewsHour with Jim Lehrer.
In October 2013, she became the first female managing editor of Time magazine.
On September 12, 2017, she announced she was stepping down as editor in chief of Time magazine.