The Russia international had an offer to join Chelsea, but the CSKA midfielder is heading to France in a £27m deal.
“Monaco and CSKA finally finally agreed on the transfer of Golovin," ASM chief Vadim Vasilyev told Sport Express.
“It's a standard five year contract. Honestly, until the last moment I wasn't sure we'd be able to complete this transfer.
“However, our main competitor was Chelsea. I believe Monaco offered more favourable conditions for the club and a more understandable sports project for Golovin. Chelsea – this is a top club, which I treat with great respect. However, the midfield in the English team is overloaded.
"In my opinion, Golovin will definitely play in any of the leading clubs in the world. But it will him some time, a transition stage."