The Premier League club were also hit with a £460,000 fine.
Chelsea were found to have breached Article 19 of the Fifa Regulations on the Status and Transfer of Players.
The ban does not prevent players being released by the club and it does not apply to Chelsea's women's and futsal teams.
'Initially, Chelsea FC was charged under Articles 19.1 and 19.3 in relation to 92 players.
Chelsea contended that the majority of the 100-plus player cases involved short-term trialists at their academy, who did not go on to sign for them.
The player was not registered with the FA and reports claim Federation Internationale de Football Association believed Chelsea misled them over dates concerning the signing of Traore's first professional contract.
Football's world governing body said two agreements the club had concluded for two of its youth players "allowed it to influence other clubs in transfer-related matters". There are exceptions if parents move to a country for non-soccer reasons or have citizenship there, but worldwide signings of minors is no longer supposed to be allowed.
As reported by AS, the Spanish club planned to adopt the same strategy it used to sign Hazard's compatriot and former Blues team mate Thibaut Courtois last August - forcing Chelsea's hand to sell Hazard at a lower cost.
It emerged in March 2018 that an inquiry into City was underway after two African players - George Davies and Dominic Oduro - gave an interview to Danish newspaper Jyllands-Posten in which they claimed to have played for the club as trainees before turning 18.
Both the FA and Chelsea could ultimately challenge any Federation Internationale de Football Association appeal ruling at the Court of Arbitration for Sport.
Chelsea can appeal this decision as well, though it's not clear yet if they will. UPDATE: Chelsea will appeal. However, following the transfer ban, Real Madrid, Hazard's most likely destination, could see their move for the player complicated. So what happens to these deals now Chelsea are not able to bring anybody in for two transfer windows? However, Barcelona were given a six-month reprieve after the club lodged an appeal which allowed them to sign Luis Suarez, Ivan Rakitic, Jeremy Mathieu, Thomas Vermaelen, Claudio Bravo and Marc-Andre Ter Stegen.