Tony Hall said he had “not taken this decision lightly” and recognized it would “divide opinion”.
However, Tony Hall added “a line has been crossed” and he “cannot condone what has happened on this occasion”.
Jeremy Clarkson, 54, was suspended on March 10, following what was called a “fracas” with Oisin Tymon.
The row, which took place in a Yorkshire hotel, was said to have occurred because no hot food was provided following a day’s filming.
An internal investigation began last week, led by Ken MacQuarrie, the director of BBC Scotland.
It found that Oisin Tymon took himself to hospital after he was subject to an “unprovoked physical and verbal attack”.
“During the physical attack Oisin Tymon was struck, resulting in swelling and bleeding to his lip.”
It lasted “around 30 seconds and was halted by the intervention of a witness,” Ken MacQuarrie noted in his report.
“The verbal abuse was sustained over a longer period” and “contained threats to sack” Oisin Tymon, who believed he had lost his job.
Oisin Tymon did not file a formal complaint and it is understood Jeremy Clarkson reported himself to BBC bosses following the incident.
After that, the BBC’s director of television, Danny Cohen, felt he had no choice but to suspend the presenter pending an investigation.
The decision caused an outpouring of support from Top Gear fans, with more than a million people signing an online petition to reinstate him.
Announcing his decision, Tony Hall said Jeremy Clarkson’s dismissal was unavoidable.
“For me a line has been crossed. There cannot be one rule for one and one rule for another dictated by either rank, or public relations and commercial considerations.”
However, he added: “This decision should in no way detract from the extraordinary contribution that Jeremy Clarkson has made to the BBC. I have always personally been a great fan of his work and Top Gear.”
In a statement, Oisin Tymon thanked the BBC for a “thorough and swift investigation into this very regrettable incident”.
“I’ve worked on Top Gear for almost a decade, a program I love,” he continued.
“Over that time Jeremy and I had a positive and successful working relationship, making some landmark projects together. He is a unique talent and I am well aware that many will be sorry his involvement in the show should end in this way.”
North Yorkshire police have asked to see the BBC’s internal report, saying it will be “assessed appropriately and action will be taken… where necessary”.
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