London Ambulance Service (LAS) attended Runnymede Hall, on the university's Isambard Complex, on Wednesday (July 22).
Police were called by LAS at around 11.20am to reports of a sudden death.
A Metropolitan Police spokesman said: "A 24-year-old man was pronounced dead at the scene.
"Next of kin have been informed.
"Police are not treating the death as suspicious and it has been referred to the coroner."
An eyewitness, who lives on the Isambard Complex, told getwestlondon: "I live in the halls opposite Runnymede and I saw two police cars with the police officers standing outside them, and the ambulance with the two paramedics in the back.
"I received a letter through my door yesterday (July 23) saying someone had died and there weren't any suspicious circumstances.
"It was quite shocking. I was surprised to see it especially after someone died [at Brunel] last year."
Residents living in the halls were sent a letter about the tragic incident.
Martyn King, operations manager of the complex, wrote: "We are sorry to report that we discovered a deceased person in one of our flats.
"There were no suspicious circumstances and there is no reason for any concern amongst our guests."
A Brunel spokeswoman confirmed that the man was not a student.
She said: "Unfortunately, we discovered a deceased person in our halls on Wednesday, in a room that had been let externally through the summer period.
"This person was not a student, and there were no suspicious circumstances.
"We offer our condolences to the family at this sad time."