The accident took place at about 0345 GMT on Sunday.
The pedestrian was taken to Glasgow Royal Infirmary but died a short time later. The 41-year-old driver of the Hackney taxi was uninjured.
The death came the day after a man was killed when his vehicle lost control and struck a crash barrier on the bridge.
David Matthews, 28, from Carmyle, died in hospital after the crash, which happened at about 0140 GMT on Saturday.
'Tragic accident'
Strathclyde Police are investigating both incidents.
Pc Colin Scott of Helen Street police station, who is leading the investigation into the death of the pedestrian, appealed for witnesses.
"At this time we are working to piece together the young man's movements and trying to establish why he was on the Kingston Bridge," he said.
"It seems to be a tragic accident."
The 21-year-old man has not yet been named.
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