The hero saw the woman fall into the river and jumped in just after midnight along with a second man who tried to save her.
Emergency services, including the coastguard and police marine units, raced to the scene in an effort to save all three people in the river.
They rescued the fallen woman - along with one of the men who jumped in to rescue her.
But emergency services were unable to find the second missing man.
Police confirmed that a body was tragically found this morning at 6am.
A City of London Police spokesperson said: “We were called at 00.12 on Saturday 24 April to reports of a woman in the River Thames close to London Bridge.
“Two men, who had witnessed the woman fall from the bridge, entered the river to try and save her.
“The Coastguard and Metropolitan Police Marine Units were able to rescue the woman and one of the men.
“Sadly, following an extensive search involving police helicopters, marine units, LFB, LAS and City Police officers, the missing man was not located.
“At 06.00 the same morning, a body was found believed to be that of the missing man.
“His next of kin have been made aware and are being supported by officers from the City of London Police.”
It comes as police continue to search for a missing 13-year-old boy who fell into the River Thames from Tower Bridge.
Specialist officers from the City of London Police, who are treating it as a missing persons case, have been leading the search for the year 8 student after he fell into the river just after 8am on Tuesday.
Witnesses told The Sun they saw the boy fall into the River Thames before one brave onlooker waded into the water to try to save him.
But the woman was only able to retrieve his schoolbag.
City of London Police said despite an “intensive search” by officers, helicopter and marine units, the boy had not yet been found.