The 27-year-old has been prolific since moving to Russia in August 2010, scoring 83 goals in 129 appearances.
Doumbia was the Russian Premier League's top scorer in 2011-12 and 2013-14, having also won two league titles and two Russian Cups in his time at the Stadion Luzhniki.
That has prompted the Roma to part with a considerable sum for his services as they go about looking to reel in Juventus at the top of Serie A.
He will not be immediately available, however, as he helps Ivory Coast at the Africa Cup of Nations, where they have reached the quarter-finals.
Italy will be the fourth nation Doumbia has taken in through his career after playing in Japan and Switzerland before Russia.
CSKA said in a statement: "PFC CSKA thanks Seydou for his contribution in the successes of the team in the past years and wishes all the best in his future career!"
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