Capello signed a two-year deal at his unveiling on Thursday afternoon and succeeds Dick Advocaat, who revealed his intention to step down and take charge of Eredivisie side PSV Eindhoven before Euro 2012.
Russia started their campaign in Poland and Ukraine with a bang by hammering the Czech Republic 4-1, but their charge fizzled out and they were eliminated in the group stage.
Capello, who has been out of work since he quit as England boss in acrimonious circumstances, is desperate to put his mark on proceedings.
"The current contract runs for two years," said the Italian. "And my next goal - to reach the finals of the World Cup in Brazil.
"After I had finished working in England, I was angry, and I wanted to continue working. I really want to achieve your goals and fight for the Cup in Brazil.
"It does not really matter with whom we compete. I now have a new beginning in a coaching career.
"I'll try to get my philosophy to match that which has brought the Russian national team success, and we will go to the World Cup in Brazil."
Capello will be looking to rebuild his reputation after a less than impressive four years with England.
After taking charge in 2008, he was initially a great success as England comfortably qualified for the 2010 World Cup.
However, matters soon went awry after a disappointing tournament that ended with a crushing 4-1 defeat by rivals Germany in the second round.
The former AC Milan, Roma and Real Madrid boss guided England to this year's tournament in Poland and Ukraine, but quit his post after the Football Association stripped John Terry of the captaincy due to the Chelsea defender being charged with making a racist remark to Anton Ferdinand.
Terry was subsequently cleared in a magistrates court trial.
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President Nikita Simonyan has given Capello his assurances that the Russian Football Union will not intervene with on-field affairs.
"The Russian Football Union will not interfere with the head coach. If Fabio decides to make (Andrey) Arshavin captain, so be it," he said.
Capello has announced his intention to live in Moscow and named Christian Panucci and Italo Galbiati as his assistants.
"The country is huge, with large populations. With plenty of talent. For advanced players, we need to create all the conditions to prepare them for performances for the national team," the 66-year-old added.
"This is my most important task. I want to give players the will to win, the desire to always fight for victory. The word 'victory' is, for me, the most important thing in my career."