Williams was raised in Winter, Wisconsin and earned an engineering degree from the U.S. Military Academy, receiving his commission in the United States Army. Williams served with the army at Johnson Space Center from 1987 to 1992 before training as a test pilot. In 1996, he was selected by NASA as an astronaut candidate and flew as a mission specialist and flight engineer aboard STS-101 in 2000.
He flew aboard the Soyuz TMA-8 mission, replacing Expedition 12 astronaut William S. McArthur. He was previously in orbit as the Expedition 13 Flight Engineer and Science Officer aboard the International Space Station. He returned to Earth on September 29, 2006. On August 24, 2006, a taped message made by him to be played at an official NASA press conference was accidentally played over the air-to-ground loop, the tape revealing that the Crew Exploration Vehicle under development to replace the Space Shuttle after 2010 would be named Orion after the famed wintertime constellation.