The team said the 38-year-old Markov signed a two-year contract to play in the Kontinental Hockey League, a week after Montreal said it would not keep the defenseman for a 17th NHL season. No salary details were given.
Markov will be reunited with Ak Bars coach Zinetula Bilyaletdinov, who coached Markov on Russia's Olympic team in 2014.
"I'm fired up to work and hope we'll be successful," Markov said.
The move means Markov could end up playing at the Olympics in February.
Russia is expected to be the favorite for an Olympic tournament without NHL players. It should have Ilya Kovalchuk and Pavel Datsyuk -- both of whom now play in the KHL -- in its team, while Canada and the United States plan to have rosters made up of professionals playing in Europe and on college and major junior teams.
Russia hasn't won an Olympic medal in men's hockey since taking bronze in 2002.
"Everybody understands it's a business and whatever decision (the) NHL made, it's their decision," Markov said last week. "But for the athletes, it's a great experience, it's a great feeling and to represent your country in such a big tournament, it's huge and it's something special."
Markov had 119 goals and 453 assists for 572 points in 990 NHL games.