The European champions also stressed that they would have no problem with Clattenburg refereeing its matches again.
Clattenburg was accused by Chelsea midfielder Ramires of saying "shut up you monkey" to teammate John Obi Mikel during an Oct. 28 Premier League match against Manchester United, but the English Football Association found that the referee had no case to answer.
Chelsea now concedes that it was wrong to publicly allege that Clattenburg used "inappropriate language" in a statement issued within two hours of the match finishing.
In attempt to clear-the-air with Clattenburg, Chelsea chairman Bruce Buck on Monday held a "constructive and open discussion" with him, the other topflight referees and Premier League chief executive Richard Scudamore.
"The club regrets not having given more consideration before issuing a statement on the evening of Sunday 28th October," Chelsea said in a joint statement with the Premier League and referees' body. "The club also regrets the subsequent impact the intense media scrutiny had on Mark Clattenburg and his family."
But the 16 topflight referees, including Clattenburg, do accept that Chelsea "had an obligation under FA rules to report the allegation," the statement said, after being received in "good faith" by a player.
That paves the way for Clattenburg to referee Chelsea matches again.
"There was recognition by all parties that the impartiality and integrity of refereeing in this country remains paramount," the statement said. "Chelsea FC made it clear they would welcome Mark Clattenburg back to Stamford Bridge in the future and (Professional Game Match Officials) would have no issue in appointing him to a Chelsea FC match going forward."
Clattenburg was cleared of any racist behaviour by the FA and the police, but English football has been blighted with racism cases recently.
A man was arrested on Wednesday after former England and Aston Villa striker Stan Collymore, who is now a radio pundit, was allegedly racially abused on Twitter.
London police are investigating anti-Semitic chants by West Ham fans at Tottenham on Sunday.
And police in northeast England have launched an investigation after a racist gesture appeared to be aimed by a fan at West Bromwich Albion striker Romelu Lukaku during Saturday's match at Sunderland.
In pictures that emerged on Tuesday, a fan appeared to make a monkey gesture at the Belgium international, who is black, after he scored West Brom's third goal in a 4-2 win. Lukaku is on a season-long loan at West Brom from Premier League rival Chelsea.
The incident comes less than a month after a Chelsea fan was banned from Stamford Bridge for making a monkey gesture in a match against Manchester United.