The prolific Senegal international will be embarking on a new challenge in the Russian capital after a deal had been agreed between the two clubs
N'Doye is seen as the ideal candidate to strengthen the Russian side's striking options, and had previously also been in negotiations with Trabzonspor over a transfer to replace the departing Burak Yilmaz.
"It's a bit of a fairytale ending here," Copenhagen sporting director Carsten Vagn Jensen told the club's official website. "It was a long road to recognition and honour for N'Doye."
"Nevertheless, we will remember him for the [three consecutive Danish] championship victories, qualification for the Champions League, and the top scorer title he earned in his time here.
"We will remember N'Doye for the great deal of effort he put in during this great period in the club's history."
The forward, who scored 82 goals in 150 appearances for Copenhagen in the Superliga since joining them from OFI Crete in 2009, will play his final match for the capital club in a friendly against West Brom on Wednesday.