The retired ex-heavyweight champion met the duo while they were filming part of the ITV2 reality television show in Las Vegas.
"He didn't want to know us, he didn't want to have a photo, but then we said, 'Hey, we're the Essex boys!" Argent told the Daily Star.
"He was like, 'What's that? Essex gangsters?' And he was a bit scared of us. Then we took a picture with him and it was all sweet after that."
In June, Tyson revealed that his one-man stage show Undisputed Truth would be turned into a television special for US network HBO.