Five other fans have been excluded from the west London stadium for up to two years for abuse at the same fixture.
Criminal charges against the supporters involved in the attack were dropped but Chelsea opted to hand down sanctions after completing their own investigation.
A video of supporters directing abuse at City winger Raheem Sterling was shared on social media and the events, along with a separate attack on Pierre-Emerick Aubameyang on December 2, sparked fresh debate into the presence of racism in football.
Colin Wing, 60, previously denied he used racist language against Sterling in an interview with the Daily Mail .
Chelsea confirmed they took that denial into account when issuing the supporter's life ban, having heard evidence from two lip reading experts who both said the language used was racially abusive.
A statement from the Premier League club issued on Tuesday read: "The club delayed reaching its decision in these cases in order to ensure that it did not prejudice the related police investigation.
"The Crown Prosecution Service has, however, recently announced that it has elected not to initiate any criminal prosecutions.
"This allowed the club to conduct its own investigation, which included seeking representations from the individuals concerned, reviewing video evidence, interviewing potential witnesses and obtaining expert opinions from two lip reading professionals. All individuals sanctioned as a result of our investigation were then offered the right to appeal and, where applicable, those appeals have been heard."
Chelsea also confirmed supporters who received a shorter sentence did so because of providing "undertakings about their future behaviour".
The statement continued: "We understand that this incident has been the subject of discussion amongst supporters, and the club appreciates that emotions can run high during matches. However, in this case the behaviour of all six individuals crossed the line of what is acceptable.
"Furthermore, in the case of the supporter who was found by the club to have used racially abusive language, there is no place for this behaviour at Stamford Bridge and a permanent exclusion was the appropriate sanction. Given the particular circumstances of this case, the club did not consider that attendance at an education course in return for a reduced sanction would have been appropriate."