The star, who is currently preparing to make his Amazon Prime debut, has settled the case out of court, Press Association reports.
The apology reads: "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."
The case was due to be heard at the Central London Employment Tribunal, according to The Telegraph.
A private hearing previously took place in November 2015, with lawyers for Jeremy and the BBC present, alongside Oisin.
Jeremy's contract was not renewed by the BBC after the incident, which is believed to have taken place when the ‘Top Gear’ presenting team were given cold meat platters instead of hot dinners, after a long day of filming on location.
A BBC investigation, led by BBC Scotland boss Ken MacQuarrie, found that Clarkson had subjected the 36-year-old to a 30-second physical attack and sustained verbal abuse.
He concluded that the producer was “subject to an unprovoked physical and verbal attack” by Clarkson, during which he was “struck, resulting in swelling and bleeding to his lip”.
Speaking days after the incident, an unnamed guest at the Yorkshire hotel where the incident took place shared their version of events, stating: “When they arrived just after 10pm Clarkson got angry. It was more like a scuffle. But he did swear using every bad word you could think of.
“The producer stood there looking quiet and embarrassed. He was being blamed for not arranging hot food.
“The general manager ended up cooking for the three presenters.”
Upon Clarkson's sacking, Tony Hall, BBC Director-General, said Clarkson had subjected an “innocent party [to] a physical altercation accompanied by sustained and prolonged verbal abuse of an extreme nature”.
In a statement following Clarkson’s dismissal in March this year, Tony Hall said it was with 'great regret that the BBC would not be renewing Clarkson's contract'.
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