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.
The contract's financial details were not disclosed but local media reported Capello would earn up to 10 million euros (£7.8m) a year.
Capello was named as Russia's next manager 10 days ago but contract wrangling delayed his installation.
- Sports & Recreation
- Dick Advocaat