Clarkson and BBC bosses had been set to give evidence in an open hearing which would have laid bare the internal working of the Corporation.
In an apology issued through Mr Tymon's lawyers Slater & Gordon - nearly a year after the fight - 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 in excess of •100,000. Clarkson and the BBC both contributed to the compensation fund.
The BBC sacked Clarkson, 55, from Top Gear following the outburst, and his co-presenters, James May and Richard Hammond, also left.
The star has tried to apologise to Mr Tymon several times before, 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 aired.
He also called on online trolls to stop abusing the producer after a number of Clarkson fans called for Mr Tymon to be sacked and said that he had a "punchable face".
However, today's statement is the first time that Clarkson has issued a full, public apology to his victim over the incident.
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."
A spokesman for the BBC said: "The action involving Mr Tymon and the BBC has been resolved.
"Oisin is a valued member of the BBC who behaved with huge integrity in dealing with the very difficult circumstances last year - a situation in which, as Tony Hall has stated, he was completely blameless.
"We are pleased that matters have now been resolved. Oisin has made an important contribution to the BBC in his 12 years with us, and we hope to see him continue to realise his potential in his role as a development executive.
"We believe Oisin has a very exciting future at the BBC."
Clarkson, May and Hammond have signed up to launch a rival motoring show on Amazon's TV service, after they were replaced as Top Gear hosts by presenter Chris Evans and a host of sidekicks including Friends actor Matt LeBlanc.
The sacked star is currently believed to be filming his new show in the Caribbean.
- Daily Mail
