The RFU had hoped to present Capello to the media on Wednesday but the presentation was pushed back a day as both sides finalised contract details.
In a brief statement on their website, the RFU confirmed a rescheduled news conference would take place in Moscow on Thursday.
The 66-year-old Italian, who quit as England manager in February, replaces Dutchman Dick Advocaat, whose tenure ended with Russia's group-stage exit from Euro 2012.
Capello, who becomes Russia's third successive foreign coach, will be tasked with blooding new players into an ageing team, something his predecessor failed to do in two years at the helm.
Russian media reports suggest Capello will earn up to 10 million euros (£7.8m) a year after signing a contract through to the 2014 World Cup, with the possibility of extending it for another two years.