'It's horrifying, that's all I can say'.
Details around the incident are sketchy, but police confirmed it happened around 9:58 London time.
"The City of London Police is currently investigating the circumstances around the death and the incident is being treated as non-suspicious," a City of London police spokesman said. "We are now working to inform the man's next of kin."
The Sun newspaper reported that the man fell from the seventh floor and landed in the lobby. The Telegraph reported that the man was believed to be married and in his 40s. The paper also noted that each floor of the exchange has walkways with gaps.
"'It's horrifying, that's all I can say," one worker told the Telegraph.
The exchange confirmed the death in a statement.
"The emergency services were called immediately and are dealing with the incident. We will continue to offer them every support and cooperation possible," it said. "Our thoughts and condolences are with the family and friends of our dear colleague. We would ask that the privacy of the family of the deceased be respected at this time. "