Chelsea also said they were sorry for the intense media scrutiny Clattenburg was subjected to following the game against Manchester United in which they complained about "inappropriate language" the referee had allegedly used towards their Nigerian midfielder John Obi Mikel.
Clattenburg was cleared by the Football Association on Thursday.
Chelsea chairman Bruce Buck held a meeting with Professional Game Match Officials Limited, which manages top English referees, and the Premier League to discuss the matter on Monday.
"The club regrets not having given more consideration before issuing a statement on the evening of Sunday 28th October," Chelsea said in a statement on their website.
"The club also regrets the subsequent impact the intense media scrutiny had on Mark Clattenburg and his family.
"The referees accept that, given Chelsea FC had received a good faith claim from one of their employees, the club had an obligation under FA rules to report the allegation."
Chelsea said they would welcome Clattenburg back to Stamford Bridge and the referees' governing body said it would have no hesitation in appointing him to officiate Chelsea games.
"There was recognition by all parties that the impartiality and integrity of refereeing in this country remains paramount," Chelsea said.
"All parties now believe it is time to draw a line under this incident, learn from it and move on for the good of all Premier League clubs, players and match officials."
