Director general of the BBC, Tony Hall, announced the news overnight and published the full findings of the corporation's internal investigation into the incident.
Speaking to BBC News, Hall praised the presenter and laid out the reasons for his dismissal: "Jeremy is a huge talent and has made an extraordinary contribution to the BBC. I've always been a huge fan of his work on Top Gear. And I also believe that his voice, and voices like his, have a place, an important place, on the BBC, but not at any price. Physical violence accompanied by prolonged verbal abuse has crossed the line. And that's why, with regret, I decided this morning that we will not be renewing Jeremy's contract."
In a published statement, Hall elaborated further: "There cannot be one rule for one and one rule for another dictated by either rank, or public relations and commercial considerations."
According to the investigation report published by the BBC: "On 4 March 2015 Oisin Tymon was subject to an unprovoked physical and verbal attack by Jeremy Clarkson. During the physical attack Oisin Tymon was struck, resulting in swelling and bleeding to his lip. The verbal abuse was sustained over a longer period, both at the time of the physical attack and subsequently."
Tymon, a producer on Top Gear, was attacked in the evening on the patio of the Simonstone Hall Hotel; the team were in North Yorkshire for a location shoot.
Clarkson's stream of "derogatory and abusive language" was directed at both Tymon and other members of the Top Gear staff, and could be heard both in the dining room and one of the hotel's bedrooms.
After the incident, Oisin Tymon believed that he had been sacked and "drove to a nearby [hospital's accident and emergency] department for examination". Over the next few days "Jeremy Clarkson made a number of attempts to apologise to Oisin Tymon by way of text, email and in person", and in the end "reported the incident to BBC management".
The report concluded: "It was not disputed by Jeremy Clarkson or any witness that Oisin Tymon was the victim of an unprovoked physical and verbal attack. He has suffered significant personal distress as a result of this incident, through no fault of his own."
Technically Clarkson has not been sacked, but rather his contract has not been renewed. The Top Gear contracts for Clarkson, May and Hammond all expire at the end of March 2015, when the show's 22nd season was originally scheduled to finish airing.
May and Hammond are involved with other shows on the BBC; it's unknown at this stage whether those shows will continue.
Hall has directed those in charge of BBC2 "to renew Top Gear for 2016", a task that the director general concedes "will be a big challenge and there is no point in pretending otherwise".
As for the current season, which was suspended with three episodes left to go, Hall has asked his team "to look at how we put out the last programmes in the current series".
Update: After the news broke, the British media conducted a doorstop interview with James May, which was broadcast on Sky News.
When asked if Top Gear would continue, May replied: "I’m sure Top Gear will continue in some way. It existed before us, it’s been reformatted several times."
As for whether he would continue with the show, May responded: "I don’t want to talk about that too much, but I think we’re very much, the three of us, a package. It works for very complicated reasons that a lot of people don’t fully understand. So, that will require a lot of careful thought."
Finally, May was confronted as to whether there was a possible Clarkson replacement that he would be prepared to work with. “Much as I think he’s a knob, I quite like working with Jeremy," the Top Gear co-host replied.