Bromley native Gboyega Odubanjo was last seen at the Shambala music festival in Kelmarsh, Northants, at about 4am on Saturday, having been invited to read poetry at the event the following day.
Officers said the case was “fast-paced and complex” with many lines of inquiry being considered.
However, the death is not being treated as suspicious.
In a statement, Northamptonshire Police said: “A body has sadly been found during the search for a 27-year-old man reported missing in Kelmarsh.
“Police officers made the discovery shortly before 9am on Thursday August 31 in the course of a specialised search of the area.
“The man had been reported missing on Sunday August 27, having last been seen at Shambala festival early the previous morning.
“While formal identification has yet to take place, the man’s family has been informed and are being supported by specially trained officers." There are not believed to be any suspicious circumstances surrounding the death.”
Det Chief Insp Johnny Campbell said: “Making a discovery of this nature is never easy for the families and friends of the missing person, or those involved in the search.
“However, this remains a live investigation as we work to understand what has happened, and speculation is not helpful for either the family or this process.”
After the news, Mr Odubanjo's family began a fundraiser in his memory which raised £32,331 in less than 24 hours.
The fundraiser, organised by Rose Odubanjo, described him as a "beloved son, brother and friend" whose life was "so suddenly cut short".
It said part of the money would go to the Gboyega Odubanjo Foundation for low-income black writers, which is to be launched by his family.
"We, the close friends and loved ones of Gboyega, express our profound sadness and grief at the loss of one of our brightest and most talented stars," it said.
"Gboyega was the source of incredible joy and laughter for all of us, and we are utterly heartbroken to hear that his life has been so suddenly cut short.
"Gboyega was inimitable. He will be remembered as a brilliant poet, inspiring friend, son and brother. He was incredibly talented; someone we will remain in awe of."