Clarkson, 55, was suspended after an alleged altercation with former producer Oisin Tymon at a hotel in Yorkshire, England.
An internal investigation followed, and BBC director general Tony Hall called the incident "a physical altercation accompanied by sustained and prolonged verbal abuse of an extreme nature" by Clarkson. Clarkson allegedly punched Tymon, who sustained a bloody lip and required hospital treatment.
Shortly after the investigation, Clarkson was officially dropped by the network.
In a statement obtained by Variety, Clarkson apologizes to Tymon.
"I would like to say sorry, once again, to Oisin Tymon for the incident and its regrettable aftermath," Clarkson says. "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."
Though details of the settlement were not made public, Variety reports it is "thought the amount is in excess of £100,000 ($139,000)," to be paid by both Clarkson and the BBC.
Since the incident, Clarkson has teamed up with former Top Gear co-hosts Richard Hammond and James May to develop a new car show for Amazon Prime that will launch this year.
Meanwhile, Matt LeBlanc will join the long-running car series as one of the new presenters for the upcoming season.
The Friends star, 48, will be the show's first non-British host in its 39-year history.
Top Gear season 23 will premiere in May on BBC America.