Mr Claydon reportedly fell from an upper tier.
On Sunday, Oasis said in a statement they were “shocked and saddened” to hear of the death of a fan.
They added: “Oasis would like to extend our sincere condolences to the family and friends of the person involved.”
The band began the Oasis Live ’25 reunion tour in July. Saturday’s concert was one of seven sold-out reunion concerts at Wembley, which has a 90,000-person capacity across three tiers.
A Metropolitan Police spokesperson said: “A man – aged in his 40s – was found with injuries consistent with a fall. He was sadly pronounced dead at the scene.
“The stadium was busy, and we believe it is likely a number of people witnessed the incident, or may knowingly or unknowingly have caught it on mobile phone video footage.”
Wembley Stadium said in a statement that medics, police and the London Ambulance service had attended to the injured man.
“Despite their efforts, the fan very sadly died. Our thoughts go out to his family, who have been informed and are being supported by specially trained police officers,” the venue said.
The band will next appear at Edinburgh’s Murrayfield Stadium for three gigs over the next week and then take their tour to Ireland, Canada, the US and Mexico before returning to Wembley on 27 and 28 September.