The six-times gold medal-winning cyclist boarded the aircraft during a visit to RAF Leuchars in Fife.
The jets, which can fly at twice the speed of sound, were based at RAF Northolt in west London to provide air security throughout the Olympic Games.
Sir Chris joined 6 Squadron for the 60-minute flight during a routine training exercise which saw him fly as high as 30,000ft. He said: “It was absolutely incredible. It’s very difficult to explain just how exciting that was to be up there and what a thrill it was.
“I feel very privileged to be asked to come here and take part in this once-in-a-lifetime opportunity. I’m full of admiration for the skills these guys have.”
The Typhoon is the RAF’s multi-role combat aircraft, with crews on stand-by all year round at the Fife base.