Clattenburg had been accused of using a racially offensive term towards Nigeria midfielder Mikel during the match at Stamford Bridge last month, which United won after a series of controversial officiating decisions.
The FA's decision to drop the case hinged around the fact that the only witness of the alleged abuse, Brazilian Ramires, does not speak English as a first language, and that other players who were closer to Clattenburg at the time - including Mikel - heard nothing.
The Metropolitan Police had earlier closed their case, launched following a complaint from the Society of Black Lawyers, after no victim came forward.
"The evidence for the allegation came from one witness, Ramires," the FA clarified in a lengthy statement.
"Ramires, whose first language is not English, explained that his instinctive reaction was to seek confirmation from John Obi Mikel as to what the referee had said.
"John Obi Mikel, who was being spoken to by the referee, was much closer to the referee than Ramires and did not hear what it is suggested was said to him.
"Three other witnesses, i.e. the other Match Officials, to whom everything said by referee was relayed via their communication equipment, are adamant the alleged words were not uttered.
"For completeness, but of lesser weight, two other players, whose first language is English and were in the vicinity, did not hear anything untoward.
"There is nothing in the video footage to support the allegation."
Clattenburg was accused of saying the word "monkey" while speaking to Mikel, and was adamant no such term was used.
He was initially also accused of insulting Spain international Juan Mata, but that was dropped by Chelsea after an internal investigation.
Clattenburg had been stood down since the alleged incident, and will not referee this weekend.
The Durham native, who is a FIFA referee and regarded as one of the top officials in Europe, expressed his relief that the case is over.
"I am looking forward to putting this behind me and concentrating on refereeing in the Premier League and other competitions," he said.
"The messages of encouragement from those inside and outside of the game have helped me through the most stressful time of my professional life.
"To know you were innocent of something but that there was the opportunity for it to wreck your career was truly frightening.
"Racism has no place in football and this experience should not discourage those to speak out if they genuinely believe they are a victim of abuse.
"However, there are processes that should be adhered to in order that any investigation can be carried out in a manner that is fair for all parties involved.
"I know first-hand the ramifications of allegations of this nature being placed into the public domain ahead of a formal process and investigation. I hope no referee has to go through this in the future."
Chelsea responded thus: "Chelsea Football Club accepts the Football Association's decision regarding Mark Clattenburg and welcomes the fact that the FA recognises the club and players were correct in reporting the matter.
"The club accepts the case is now concluded and notes the FA states the allegation was made in good faith.
"Chelsea FC has a duty of care, as do all employers, to act responsibly when such allegations are reported by employees.
"We did not take the decision to lodge a formal complaint with the FA lightly and followed the correct processes and protocols throughout."
However referees' union Prospect are asking Chelsea for a full apology and compensation on behalf of Clattenburg.
The club have been criticised for failing to apologise to Clattenburg, who also claimed initially that he had abused Spain international Juan Mata.
Respected Daily Telegraph sports writer Henry Winter tweeted: "#cfc fail to apologise to Clattenburg despite making his life a misery with an unfounded allegation. Gourlay's an embarrassment to football" in relation to Ron Gourlay, the Blues chief executive.
Separately, Mikel has been charged for his behaviour after the match, when he was alleged to have confronted Clattenburg in an angry exchange in his office.
He has accepted the charge and requested a personal hearing.