The club made the decision to punish Terry after he decided on Friday not to appeal against his four-match ban for racially abusing Ferdinand - however, the club are keeping their sanction secret. And Cole, Terry's team-mate for club and country, has been fined £90,000 over his foul-mouthed Twitter attack on the Football Association following the verdict in the Terry trial.
Terry has apologised for the language he used after announcing he will not challenge the ban and fine of £220,000 issued by an independent Football Association regulatory commission two weeks ago.
Terry has not however apologised directly to Ferdinand.
In a bad day for the club, the FA also confirmed the fine on Cole after the defender admitted a charge of making a Twitter comment that was improper and/or brought the game into disrepute.
Read in full: Cole fined for Twitter outburst
The Chelsea defender had labelled the FA a "bunch of t***s" on the social networking site after an independent regulatory commission of the governing body investigating the John Terry racial abuse case had cast doubt on Cole's evidence.
In a statement, Chelsea also indicated they have taken further steps against their captain beyond the sanction.
The statement said: "Chelsea Football Club believes John Terry has made the correct decision by not appealing against the FA judgment relating to language he used at the QPR match last October.
"Chelsea also appreciates, and supports, John's full apology for the language he used. The club firmly believes such language is not acceptable and fell below the standards expected of John as a Chelsea player.
"The board has conducted its own investigation into the matter, and considered the various issues involved. The board has taken further disciplinary action in addition to the four-match suspension and £220,000 fine imposed by the FA. In accordance with our long-standing policy, that disciplinary action will remain confidential."
The FA suspension means Terry will miss Chelsea's games against Tottenham, Manchester United - both in the Premier League and Capital One Cup - and Swansea.
In an attempt to close a lid on the Terry case, Chelsea later added: "Chelsea enjoys support all over the world. We have players and supporters from many different countries and cultures and our club is committed to eradicating all forms of discriminatory behaviour. John is fully committed to continue supporting that ongoing work."
Terry was found guilty by the FA commission of calling Ferdinand a "f****** black c***" during a Barclays Premier League match between Chelsea and QPR on October 23 last year.
He had earlier been cleared in magistrates court of a racially-motivated public order offence.
The three-man panel had ruled there was "no credible basis" for Terry's claim he had only been repeating words he thought QPR defender Ferdinand had accused him of saying, and labelled his defence "improbable, implausible and contrived".
The commission also questioned why Terry's team-mate Ashley Cole had changed his statement to give more support to Terry's story, sparking the eventual furious response from the England defender.
Cole's outburst two weeks ago was retweeted more than 19,000 times and provoked large condemnation from the footballing world.
He apologised to FA chairman David Bernstein, who only two days earlier had revealed that the England squad had been spoken to about a new code of conduct.