The British Sunday Times newspaper said the pair had approached the unnamed royal family member and demanded £50,000 ($100,000) not to publicize a video allegedly showing the royal engaged in a sex act.
The blackmailers also claimed to have evidence suggesting the royal had supplied an aide with an envelope containing cocaine, the newspaper said.
The newspaper said it could not identify the royal family member for legal reasons.
The Sunday Times said the blackmailers' target contacted police and two suspects were arrested at a London hotel on September 11 after an undercover police operation.
Buckingham Palace did not comment on the allegations, but former Royal Press Secretary Dickie Arbiter told British broadcaster SKY that things were now "in police hands."
"The two individuals have appeared before Westminster Court in September. They are due to appear in court at the Old Bailey (the Central Criminal Court) in December," Arbiter said.
"It is a police matter," he added. "It is now out of the hands of Buckingham Palace."
In response to queries about the report, London police confirmed that two men, aged 30 and 40, had appeared at a London court on September 13 charged with blackmail.
They were ordered detained until a hearing at London's Central Criminal Court on December 20.
The police would give no details of the case or identify the suspects.