The actor, who is promoting his new film King Richard, appeared on the latest episode of the BBC chat show that was broadcast on Friday (26 November).
While there, he shared a story about pushing through the crowd at an opening of a new Planet Hollywood restaurant so that he could get advice on how to become an actor from Schwarzenegger, Sylvester Stallone and Bruce Willis.
“They were standing and talking,” Smith explained. “I walked into the crowd, I was like, ‘Hey guys, I’m sorry. I want to do what you’re doing – I want to be the biggest movie star in the world and I know if anybody can tell me how to do it, you guys can.’”
He continued: “They looked at one another [and] I guess in secret movie star message they communicated that Arnold was going to answer me.”
Here, Smith launched into his impression of the Terminator actor.
“If you’re going to be a movie star, the movies can’t only be successful in America,” Schwarzenegger told a young Smith. “You’ve got to go to every country in the world. You have to think of yourself as a politician running for biggest movie star in the world.”
Norton and the actor’s fellow guests, Richard Osman and comedy couple Chris and Rosie Ramsey, erupted into laughter at his impression.
“Damn, Will Smith’s Arnold impression is amazing,” one impressed viewer wrote on Twitter, with another calling it “solid”.
“It’s Arnold possessing Will and speaking through him!!” another quipped.
Jaden’s request came after the pair co-starred in the 2013 film After Earth, which Will described as “an abysmal box office and critical failure”.
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“And what was worse was that Jaden took the hit,” Smith wrote in the memoir, adding: “Jaden had faithfully done everything that I’d instructed him to do, and I had coached him into the worst public mauling he’d ever experienced.”
The Independence Day actor described how his “heart shattered” when Jaden asked him to become emancipated, a decision the now 23-year-old star “ultimately decided against”.
Elsewhere, the actor claimed that he had so much “rampant sex” after his first break-up that the act would make him physically sick.
The episode is available to stream on iPlayer now.