The 22-year-old has been heavily linked with a move to Stamford Bridge over the summer, with one report last week even claiming that the Premier League side had agreed personal terms with the Russian.
According to Sport Express - a publication in his homeland - Golovin has now decided not to sign for the Blues and will instead pen a deal with the wealthy French side.
Monaco vice president Vadim Vasilyev is quoted by the newspaper as saying: "Monaco and CSKA Moscow today agreed on the transfer of Golovin on a five-year contract.
"Honestly, until the last moment I was not sure that I would be able to co-ordinate this transfer.
"I believe that Monaco offered more favourable conditions for the club and a more understandable project for the player."
Golovin, who has been with CSKA since 2012, played a starring role for Russia at this summer's World Cup as the home nation made it through to the quarter-final stage of the tournament.