A 37-year-old man was arrested at his home in Kent by officers during dawn raids by officers from Operation Elvedon. A 34-year-old man was also arrested in south east London.
Trinity Mirror has already confirmed that the 37-year-old detained by police is Sunday Mirror crime reporter Justin Penrose.
The other person is known to be Daily Star Sunday deputy news editor Tom Savage.
In a statement, Trinity Mirror said: "We have been informed by the police that Justin Penrose was arrested this morning on suspicion of alleged payments to public officials. We are co-operating fully with the police."
Police are also said to have searched the offices of the Sunday Mirror and taken possession of various items from Penrose's desk, including his computer.
The publisher added: "Following a prearranged meeting at 11am the police now have in their possession various items from Justin Penrose's desk including his computer. There is no further comment to make at this stage."
Express Newspapers, publisher of the Daily Star Sunday, confirmed that Savage had been arrested by Operation Elveden, the police investigation into corrupt payments made to police and public officials.
An Express Newspapers spokesman said: "We can confirm that one of our reporters was arrested this morning as part of Operation Elveden and we are working closely with the authorities in relation to this matter."
The arrests are part of an expansion of Operation Elveden beyond just Rupert Murdoch's News International - the previous focus of suspicion on alleged phone hacking and illegal behaviour.
Penrose is not the only Mirror journalist arrested in the operation, as Grieg Box-Turnbull, who worked for the paper until March, was detained last week.
In total, 41 people have been arrested as part of Operation Elveden, including prison officers, police officers and army officials, as well as journalists.
In a statement, Scotland Yard said: "Today's arrests relate to suspected payments to a public official and are not about seeking journalists to reveal confidential sources in relation to information that has been obtained legitimately.
"A 37-year-old man was arrested at his home in Kent, and a 34-year-old man at his home in south-east London at approximately 6am this morning on suspicion of conspiracy to corrupt (contrary to the Prevention of Corruption Act 1906) and of conspiracy to cause misconduct in a public office (contrary to common law)."