They will not appeal against their charges, but Jose will appeal against his with the full backing of the club.
The Premier League issued unprecedented fines for breaching rules by meeting at a London restaurant in January.
Chelsea were fined £300,000 and given a suspended three-point deduction for their involvement.
Arsenal defender Cole was handed a £100,000 fine, while Blues manager Jose Mourinho will have to pay £200,000.
Chelsea full statement is as follows: "Chelsea Football Club has today confirmed that it will not appeal the verdict and sanctions handed down to it by the Premier League independent commission two weeks ago. Although at the time we indicated an appeal was likely, and we were advised there were strong grounds for one, the Chelsea board of directors came to the conclusion that the greater interests of football were served by the club drawing a line under the issue.
"In arriving at that position, the Chelsea board held helpful and amicable discussions with colleagues from the wider football community.
"Regarding the verdict and sanctions against José Mourinho, these will be
appealed by José, with the full support of the club. Chelsea believes José
should not have been charged separately as this did not happen in previous cases of a similar nature. Both José and the club also believe that the sanctions against him were disproportionate to the alleged offence."