The country's football association said Slutskiy, 44, signed a contract until the end of the Euro 2016 qualifying campaign. He will continue to coach CSKA Moscow, after his club gave him the go-ahead to combine the two roles.
However, the national coach would not be able to combine the roles when preparing Russia for the 2018 World Cup, which the country will be hosting, according to Russian sports officials.
Capello, 69, who managed England at the 2010 World Cup, took over as Russia coach in July 2012 but his contract, which was to expire at end of the 2018 tournament, was terminated last month after the team's poor performance.
The Italian led Russia to their first World Cup in 12 years after taking them to Brazil in 2014 but the team failed to win a single match and crashed out at the group stages.
The team's form has not improved since then and they suffered a loss at home to Austria in their Euro 2016 qualifier.
The contract severance was a costly exercise and Russian media reported football officials had to call for help from businessmen, including steel tycoon Alisher Usmanov, to pay Capello between 8-15 million euros as departure fee.
Slutskiy had earlier coached Olimpia Volgograd, Uralan Elista, FC Moscow and Krylia Sovetov Samara before taking over CSKA in 2009. Under his management the Armymen have won both the Russian Premier League title and the Russian Cup twice.
"We have said many times that at this stage, a Russian coach should take over the national team," Russian Sports Minister Vitaly Mutko said in a statement.
"Given Leonid Slutskiy's successful and effective work at CSKA, I think he is exactly the one who is capable of the task of getting into the Euro-2016."
Russia are currently third in their Euro 2016 qualifying group G, with eight points from six matches. Their next match is against Sweden on Sept 5 in Moscow.
"Given the difficult situation the national team find themselves in, it was impossible for me to turn down this offer," Slutskiy told CSKA Moscow's official website (www.pfc-cska.com).
(Writing by Dmitry Zhdannikov; editing by Amlan Chakraborty)
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