Police were called to the bridge shortly after after 6pm on Friday over initial fears of a potential suicide attempt.
It is alleged the 21-year-old jumped off the bridge on the Dundee side and them swam to shore while his friend filmed.
The man was traced uninjured by police officers nearby.
Police warned jumping from the bridge was an act of “unbelievable stupidity” as the water had dangerously strong currents.
Sergeant Andrew Sheppard, said: “Even when the tide is out and the water apparently calm, there are incredibly strong currents under the Tay Bridge that could have swept this man away to his potential death.
"He has caused considerable distress and alarm to bridge staff and passers-by who witnessed him jump from the bridge, and has also caused emergency services to respond to
what was thought to have been an extremely serious incident when they may have been needed elsewhere.
“To anyone who thinks this kind of thing is funny or a joke, I can assure you that it is not, and you are dicing with death with idiotic stunts of this kind.”