Felsenthal was born in Memphis, Tennessee, where he attended Memphis University School. He earned an A.B. degree from Princeton University, a J.D. from Harvard Law School, and an M.A.L.D. from The Fletcher School of Law and Diplomacy.
Felsenthal began his career at The Wall Street Journal, where he covered the U.S. Supreme Court and later became an editor overseeing the Journal's efforts to expand its consumer and lifestyle coverage. He was the founding editor of the Personal Journal section, guiding work that led to two Pulitzer Prizes, and later oversaw news strategy and integration of the print and digital teams. He was named Deputy Managing Editor of the Journal in 2005. In 2008, he worked with Tina Brown to launch The Daily Beast as the first executive editor. He joined TIME in 2013 as Digital Managing Editor, where he led an expansion that established a 24/7 news and video operation. In 2016, he became Group Digital Director for Time Inc., overseeing 12 news and lifestyle sites. He became the 18th editor of TIME in September 2017, succeeding Nancy Gibbs.