The TV stars feuded for a long time, brawling at an awards ceremony in 2004 and rowing on a Concorde flight, but have since buried the hatchet.
Opening up about the time Clarkson hit him, Morgan said on the Big Fish podcast: "That scar on my head is where he punched me in the head, we're not exactly best buddies, although we get on fine now."
Morgan said that it came about when he was editor of the Mirror and had published photographs of Clarkson that he wasn't pleased with, "so next time he saw me he punched me in the head, which I thought was perfectly reasonable".
The star, 57, said that he could have “played the victim” after the altercation.
He said: "But I went, you know what? Fair enough, I'd of probably done the same."
Clarkson, 62, later addressed the row in an interview with Sir Michael Parkinson, saying it had been "the first time I’ve hit anybody ever".
Morgan went on the programme to try and win money for charity and confessed he was worried about asking his old enemy for help by using the Ask the Host lifeline.
“I can think of a million reasons why I shouldn't trust you, including this scar on my forehead," he quipped.
"And there's your broken finger, from when he struck me.”
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