The Grand Tour trio insisted Jeremy Clarkson was not "technically" fired from BBC's Top Gear in their first episode released on Friday morning.
James May and Richard Hammond joined him in the debut episode - titled The Holy Trinity - on Amazon Prime Video after parting ways with the BBC when Clarkson punched a producer.
The opening sequence - rumoured to have cost £2.5 million - saw Clarkson leave a shiny London office under storm clouds and take a black cab trip while listening to radio reports of his demise.
He boarded a plane to Los Angeles to join his sidekicks and they drove in a vast convoy with I Can See Clearly Now playing in the background to their own "Burning Van" festival in a Californian desert.
From the stage, they listed a string of jobs that Hammond and May have been fired from.
Hammond, who described Clarkson as "basically a shaved ape in a shirt", said the 56-year-old "technically is the only one of us never to be fired by anyone".
Clarkson replied: "The good thing is it's very unlikely I'm going to be fired now because we're on the internet, which means I could pleasure a horse ... dog?"
He went on to describe their roles in the series - where they will present each episode in a different country - as being like "gypsies".
"Only the cars we drive are going to be insured," he added.
The action-packed opening episode saw the trio test the McLaren P1, Porsche 918 Spyder and Ferrari LaFerrari sports cars on their new track in Portugal.
Clarkson gave Top Gear producer Oisin Tymon a bloody lip in a bust-up in March last year.
The presenter's contract was not renewed by the BBC and his co-hosts followed him to Amazon's subscription streaming service.
Clarkson issued a formal apology in a deal to settle a racial discrimination and personal injury claim.