"Russia's national coach has been appointed - he is Fabio Capello. We wish him success in his new job," Arshavin wrote on his personal website.
The 31-year-old Arsenal player, widely considered Russia's most influential footballer, could have had inside information into the affairs of the Russian FA (RFU).
However, the Arsenal forward might have jumped the gun announcing Capello's appointment as according to the official RFU line, talks with the 66-year-old Italian will continue next week.
Capello, who quit as England boss in February, came to Moscow on Thursday to meet Sports Minister Vitaly Mutko and acting RFU chief Nikita Simonyan.
Mutko, who described the talks as "productive", said the RFU would name a new coach early next week.
Local media reports on Saturday claimed RFU would hold the final round of negotiations with Capello on Tuesday.