One of the men is Justin Penrose, a reporter for the Sunday Mirror tabloid, Penrose's employers said.
"We have been informed by the police that Justin Penrose was arrested this morning on suspicion of alleged payments to public officials," said a spokesman for the newspaper's owner Trinity Mirror.
"We are co-operating fully with the police."
Scotland Yard said that in dawn raids a 37-year-old man was detained at his home in Kent, southeast England, and a 34-year-old man at his home in London, but did not identify them.
Both were being questioned at separate police stations on suspicion of conspiracy to corrupt and conspiracy to cause misconduct in a public office.
A source close to Murdoch's British newspaper wing News International said the other journalist did not work for the company.
Operation Elveden, Weeting & Tuleta
The arrests bring to 41 the total number arrested under Operation Elveden, Scotland Yard's investigation into allegations of inappropriate payments by journalists to police and public officials.
The operation is being run alongside Operation Weeting, an investigation into phone-hacking at British newspapers, and Operation Tuleta, covering alleged computer hacking.
More than 60 people have been arrested under the three investigations, including Rebekah Brooks, a former top aide to Murdoch and friend of British Prime Minister David Cameron and his former media chief Andy Coulson.
Scotland Yard set up the three investigations in the wake of the phone-hacking scandal that forced Murdoch's News of the World tabloid to close last July.
Australian-born tycoon Murdoch, 81, closed the 168-year-old Sunday newspaper after revelations that it had accessed the voicemail of a murdered schoolgirl, as well as dozens of public figures.