The broadcasting launched an investigation into the Burma TV special and ruled in July that the presenter had "deliberately employed the offensive word to refer to the Asian person".
The regulator decided there was "insufficient context to justify the broadcast of this material" and that the BBC did not apply generally accepted standards to protect viewers from offensive material.
The programme's executive producer, Andy Wilman, previously apologised for the use of the term, saying it had been intended as a "light-hearted word-play joke" and that the team had been unaware the term was considered offensive.
As the latest controversy involving Clarkson and Top Gear came to light, the television presenter took to his Twitter page to express his love for the country Chile.
The presenter was referring to the help the Top Gear team received from the country's security in allowing them into the country as they fled Argentina.
The second-part Christmas special of Top Gear, which aired last night, showed the crew's hasty departure from Argentina.
Clarkson, Hammond and co-presenter James May were forced to flee the country after angry mobs started targeting them when Clarkson displayed a numberplate of H982 FKL - an apparent reference to the 1982 Falklands War.
The Top Gear team were in Argentina as part of their mission to reach the bottom of South America in V8 sports cars, build a "stadium" from shipping containers and play a game of "car football".
In the wake of the Top Gear's visit to South America, leading Argentine daily newspaper, Clarin, has accused Clarkson of continuing to strain the relationship between Britain and Argentina.
Watch: Clarkson denies using n-word
It dubbed the BBC's Top Gear special "the programme of controversy".
And another newspaper, La Nacion - referring to the diplomatic row the programme generated and referring to the Falklands by their Spanish name - blasted: "The BBC broadcast the Top Gear programme that poked fun at Argentinians over the Malvinas."
Argentine news channel TN also headlined its coverage by saying: "They broadcast the controversial programme."
It added: "Despite the Argentine government's protests, the BBC broadcast the second part of the Top Gear programme filmed in Patagonia. They showed the team fleeing after the provocation over the Malvinas."
Last night's Top Gear Christmas special also created debate on social media.
One Argentine wrote on Facebook: "I've just watched the programme. Apart from the offensive numberplate and the stupidity of the presenters, I've seen some excellent images, perhaps some of the finest I've ever seen of the area.
"The quality of the filming is exceptional and the choice of routes and places along the way impeccable. You see the programme and want to go there."
But the post drew an immediate response from another who claimed: "I go to Patagonia twice a year to fish and I have thousands of photos. I don't need these Top Gear clowns to enjoy the naturalness of what thank God is Argentinian and not pirate-owned.
"I'm sure they made this programme out of envy because of the rubbish country they have and the fact they like rubbishing everyone else."
It is the latest controversy to hit Clarkson, who was forced to apologise earlier this year when he was given a formal warning by the BBC about his conduct.
The corporation apparently put him on his final warning in May for "appearing" to use the n-word in unaired Top Gear footage.
It came after the unaired footage of him using the "eeny meeny" nursery rhyme to compare two sports cars was leaked to the media.
Historically, the rhyme was "Eeny meeny miny moe, catch a n***** by his toe", and Clarkson said he "mumbled" in two takes to avoid using the racist term - which made it sound like he was saying it.
In the third, which was broadcast, he said the word "teacher" instead.
In the wake of the scandal, he said: "I've been told by the BBC that if I make one more offensive remark, anywhere, at any time, I will be sacked."
- Daily Mail
