Born Kostya Gessen, he, his parents, and sisters moved to the United States in 1981 "to escape state-enforced anti-Semitism and settled in the Boston area, living in Brighton, Brookline, and Newton, Massachusetts.
He graduated from Harvard College, where his major was Russia in America. Gessen completed the course work for his MFA in Creative Writing from Syracuse University in 2004 but did not receive a degree, having failed to submit "a final original work of fiction".
Gessen has written about Russia for The Atlantic and the New York Review of Books. In 2005, Dalkey Archive Press published Gessen's translation of Svetlana Alexievich’s Tchernobylskaia Molitva (Voices from Chernobyl), an oral history of the Chernobyl nuclear disaster.
In an August 2008 interview, Gessen revealed that he is moving back to Russia for a year, returning in June 2009, while his sister attends graduate school in the United States.
His mother was a literary critic, and his father was a computer scientist.. His sister, Masha Gessen (born 1967), is the author of Ester and Ruzya: How My Grandmothers Survived Hitler's War and Stalin's Peace (a.k.a. Two Babushkas). His maternal grandmother, Ruzya Solodovnik, was a Soviet government censor of dispatches filed by foreign reporters such as Harrison Salisbury; his paternal grandmother, Ester Goldberg Gessen, was a translator for a foreign literary magazine.