Chelsea say they "regret" the way they handled their accusation that referee Mark Clattenburg used racial language towards midfielder John Mikel Obi.
The Blues also regretted the subsequent "intense media scrutiny" faced by Clattenburg and his family.
The club also indicated they would be happy for Clattenburg to referee at Stamford Bridge in future.
Clattenburg's boss, the Professional Game Match Officials Limited (PGMOL), also said it would have "no issue" in appointing him to Chelsea fixtures.
A joint statement by the Premier League, PGMOL and Chelsea said: "It is time to draw a line under this incident."
Clattenburg missed four weekends of Premier League matches while the FA investigated Chelsea's complaint, but will return to referee Norwich's match at Southampton on Wednesday.
In Tuesday'sjoint statement, Chelsea insisted they had been duty bound to report the allegation to the FA.
"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," the statement read.
However, Chelsea acknowledged that making the allegations public immediately after the game led to unwelcome press attention towards Clattenburg and his family.
"The club regrets not having given more consideration before issuing a statement on the evening of Sunday, 28 October," the statement continued. T"he club also regrets the subsequent impact the intense media scrutiny had on Mark Clattenburg and his family."
The meeting between PGMOL, the Premier League and Chelsea took place on Monday at England's National Football Centre, St George's Park.
PGMOL were represented by general manager Mike Riley and all 16 top-flight referees, the Premier League by chief executive Richard Scudamore and Chelsea FC by club chairman Bruce Buck.
Referees' union Prospect welcomed the joint statement and said the use of the word "regrets" was "tantamount to, and accepted by Mark and the Select Group [of referees], as an apology".
"Importantly the statement also refers to Chelsea's willingness to welcome Mark back to Stamford Bridge," Prospect continued.
"This was an important move forward in confirming Chelsea's recognition of Mark's integrity and impartiality."
The 37-year-old always denied the charges and the Metropolitan Police dropped its own inquiry earlier this month.
Clattenburg admitted that he feared that the allegations could have brought an end to his career as a referee.
"To know you were innocent of something but that there was the opportunity for it to wreck your career was truly frightening," he said in a statement after being cleared by the FA.
Upon clearing Clattenburg, the FA charged Mikel with misconduct following his involvement in the incident.
Chelsea have indicated he will not deny the charge but will request a hearing to "explain the mitigating circumstances".