The 44-year-old replaced Fabio Capello and guided the national team to the European Championships and is now set to remain in the role.
Leonid Slutsky will continue to combine his positions as coach of CSKA Moscow and Russia until the end of Euro 2016.
The 44-year-old was drafted in on a short-term deal in August following Fabio Capello's dismissal for poor results at the start of the country's qualifying campaign for the European Championships.
Slutsky originally agreed to take the helm alongside his duties with CSKA up to the end of the process, leading the national team to four straight wins and automatic qualification for Euro 2016.