Mr Cohen defended the star despite a string of incidents in which Mr Clarkson used questionable language.
The presenter mumbled the N-word in a racist version of the children’s rhyme “Eeeny, Meeny, Miny, Moe” in an unaired clip from the show that emerged earlier this year, called an Asian man “a slope” during a programme about Burma that was broadcast and named his black dog “Didier Dogba” after Chelsea footballer Didier Drogba.
Mr Cohen said in a letter to The Guardian: “Whilst, Jeremy and I disagree on the language some have recently found very offensive I do not think he or anyone on the Top Gear team are racist.”
The executive admitted that it was “no secret” that there had been “some significant issues” with Top Gear.
“The BBC has taken them seriously and has left no one associated with the programme under any illusion just how seriously,” he said.
“Top Gear is an extraordinary television programme, loved by millions of viewers around the world. I want Top Gear to maintain its unique take on the world but more controversies of this nature would serve no one well.
“The focus now is on the future and continuing the great success of Top Gear with audiences.
“I’m confident the hard-working, high-quality production team will deliver this.”
His comments were made public after he ordered an internal review into the culture of Top Gear in the wake of the complaints about racism.
Video: Jeremy Clarkson apology
Last month, the regulator Ofcom found that the “slope” comment had breached broadcasting rules.
In the show, broadcast in March, Clarkson and the other Top Gear members built a wooden bridge with the help of local people.
“That is a proud moment, but there's a slope on it,” Clarkson said as the camera panned to show a local man walking on the bridge. “Slope” is a derogatory term for Asian people. BBC producers had tried to dismiss the remark as “light-hearted wordplay”.