Williams said he saw the object on 27 April at about 22:40 GMT over West Africa while watching for the approaching Progress MS-34 cargo craft.
He posted photos and video showing the bright object streaking through the upper atmosphere before splitting into smaller pieces, calling it a striking light show.
The fireball was likely the re-entering upper stage of the Soyuz rocket that launched Progress 95, which delivered about three tons of supplies to the station.
How could the new Dream Chaser space plane make fiery rocket re-entries like this a relic of the past?
What invisible chemical footprint do these increasingly frequent 'light shows' leave in our upper atmosphere?
With space traffic growing, what international laws prevent rocket debris from falling on populated areas?