"We dealt with this matter some time ago, the programme apologised at the time and explained the context, and we are now focusing on delivering another series of one of Britain's best loved shows."
Clarkson used the word "slope" in a play on words about a makeshift bridge that the programme had constructed across the River Kwai in Thailand.
As an Asian man walked towards him, the presenter looked at the bridge and said: "That is a proud moment... but... there is a slope on it."
Ofcom received two complaints that the expression was racist and offensive. The watchdog took the view that "the word 'slope' is an offensive and pejorative term for a person of East Asian descent, which originated during the Vietnam War".
But in their defence, Top Gear's programme makers claimed they thought the term amounted to "mere slang". They said they were not aware the word had "the potential to cause offence particularly in some countries outside the UK".
The BBC also reminded Ofcom that Andy Wilman, the long-standing executive producer of Top Gear, had already issued a public statement apologising for any offence caused to viewers by the programme, which was broadcast in March.
"When we used the word 'slope' in the recent Top Gear Burma Special it was a light-hearted word play joke referencing both the build quality of the bridge and the local Asian man who was crossing it," said the statement.
"We were not aware at the time, and it has subsequently been brought to our attention, that the word 'slope' is considered by some to be offensive and although it might not be widely recognised in the UK, we appreciate that it can be considered offensive to some here and overseas, for example in Australia and the USA."
In ruling that Top Gear had breached broadcasting rules, the regulator said it had considered that the show was "known for its irreverent style and sometimes outspoken humour" and that it "had previously used national stereotypes as a comedic trope, particularly to describe the characteristics of cars".
But it said the programme had failed to research the meaning of the offensive term and there was "insufficient context to justify the broadcast of this material".
Other Top Gear gaffes
July 2014: Ofcom finds Top Gear has breached broadcasting rules after Clarkson commented on there being a "slope" on a makeshift bridge across the River Kwai as an Asian man came into shot.
May 2014: Clarkson claims to be "mortified" after unbroadcast Top Gear footage emerges showing him using the N-word while reciting the rhyme "Eeny Meeny Miny Moe".
December 2011: The Indian High Commission complains to the BBC after a Top Gear Christmas special mocks Indian culture.
February 2011: The Mexican ambassador to the UK complains of "outrageous, vulgar and inexcusable insults" to his country after Clarkson and his colleagues made a string of jokes about Mexico's national character.
- Independent