The Metropolitan Police force said officers and paramedics responded to reports of an injured person just before 10.30pm local time on Saturday.
It said a man in his 40s was found "with injuries consistent with a fall." He was pronounced dead at the scene.
The force urged anyone who saw what happened or caught it on phone video to contact police.Â
"We are shocked and saddened to hear of the tragic death of a fan at the show last night," Oasis said in a statement, offering "sincere condolences to the family and friends of the person involved".
A witness told the Daily Mail: "It was horrendous.
"The guy fell from a balcony. Paramedics came rushing over. There was a lot of screaming and shouting.
"It was a big fall. God knows how it happened. It was so tragic. I don't know how on Earth it happened.
"It was heartbreaking. He was only young."
The Britpop icons' first tour in 16 year s kicked off July 4 in Cardiff, Wales. Saturday's concert was the fourth of seven planned shows at Wembley.
Stadium management said Sunday's gig would go ahead as planned.
with PA