The 19-year-old left his family home in Ladbroke Grove, west London, on the evening of Monday 22 March, boarded a bus, and later took a 20-mile taxi ride from the W2 area of the capital to a residential street in Loughton, Essex.
Specialist police search officers and dog units have been searching Epping Forest after CCTV captured him walking towards the forest in the early hours of Tuesday 23 March - the last time he was seen.
Police say the body has not yet been identified but that Mr Okorogheye's family have been told of the development and they are being supported by specialist officers.
The Met said in statement: "On the afternoon of Monday 5 April the Met was informed by colleagues from Essex Police that the body of a man had been found in a pond in Epping Forest.
"Enquiries are under way to identify the body. Officers remain at the scene and enquiries continue."
The Oxford Brookes student, who has sickle cell disease, had been struggling to cope with shielding for the past year and it is believed he did not take his daily medication with him.
Detectives have said there had not been any activity on his phone since he disappeared.
Mr Okorogheye's mother, Evidence Joel, told Sky News on Thursday her son had never mentioned Loughton and she thought he went there to "meet somebody".
"Someone was waiting for Richard," she said.
Ms Joel said she "most definitely" thought he had met somebody online as she had heard him laughing while playing his PlayStation 5 and being "very happy" while talking to someone.
She said she did not know anything specific about the person.