Detective Chief Inspector April Casburn was charged with misconduct for phoning the News of the World and offering to pass on information about whether London's police force would reopen its stalled phone-hacking investigation.
Prosecutors said the tabloid did not print a story based on her call and no money changed hands. However, they said, she had committed a "gross breach" of the public trust by offering to sell the information.
Casburn, 53, also was accused of trying to ruin the inquiry, which centered on journalists at the now-defunct News of the World, by leaking information to the press.
The Metropolitan Police said in a statement that selling confidential information to journalists for personal gain would not be tolerated. The statement said the detective had "abused" her police position.
"Casburn proactively approached the News of the World, the very newspaper being investigated, to make money," the police statement said. "She betrayed the service and let down her colleagues."
The statement said vital information on the Casburn case was given to police by the Management and Standards Committee at Murdoch's News Corp.
Casburn, who managed the Metropolitan Police terrorist financing investigation unit, had admitted contacting the newspaper but denied that she offered confidential information or sought payment.
Jurors at Southwark Crown Court found her guilty of one count of misconduct. She will be sentenced later this month.
The long-running phone-hacking scandal has led to dozens of arrests and to criminal charges against prominent journalists, including Prime Minister David Cameron's former communications chief.
It has involved allegations of illegal snooping on celebrities, crime victims, politicians and others. Media mogul Murdoch closed the News of the World tabloid in July 2011 after many of its misdeeds were exposed.