Oisin Tymon launched the action against Mr Clarkson and the BBC after the presenter gave him a bloody lip in a bust-up last March.
Mr Clarkson reportedly flew into a rage after being told he could not order steak after a day of filming, calling Mr Tymon a “lazy, Irish c***” during the fracas at a North Yorkshire hotel.
In an apology issued through Mr Tymon’s law firm, Slater and Gordon Lawyers, Clarkson said: “I would like to say sorry, once again, to Oisin Tymon for the incident and its regrettable aftermath.
“I want to reiterate that none of this was in any way his fault.
“I would also like to make it clear that the abuse he has suffered since the incident is unwarranted and I am sorry too that he has had to go through that.
“I am pleased that this matter is now resolved. Oisin was always a creatively exciting part of Top Gear and I wish him every success with his future projects.”
No details of the settlement were given, but it is understood to be more than £100,000.
Mr Clarkson and the BBC both contributed.
The settlement means there will not be an employment tribunal hearing, which could have heaped further embarrassment on the popular presenter.
The BBC sacked Mr Clarkson, 55, from Top Gear following the bust-up, prompting his co-presenters James May and Richard Hammond to quit the show.
Mr Clarkson had reportedly tried to apologise to Mr Tymon in the past and last June he tweeted that he was “so sad and sorry it’s ended like this” after his last Top Gear show with Hammond and May was screened.
Mr Tymon’s lawyer, Paul Daniels, said: “The action involving Mr Tymon has been concluded. Oisin is keen to put the matter behind him now that it has been brought to a close.
“Oisin greatly appreciates all of the support he has received, including from the BBC. He remains focused on the creative work he loves at the BBC.”