Amazon said the motoring show, starring ex-BBC presenters Jeremy Clarkson, Richard Hammond and James May, was its most popular show. That title was previously held by The Man in the High Castle.
Both shows are only available to viewers paying for Amazon Prime. The tech firm slashed the subscription fee from £79 to £59 a year ahead of The Grand Tour opener.
Would-be fans could also receive teasers via Alexa, Amazon's smart assistant. Anyone downloading The Grand Tour skill onto the Amazon Echo smart speaker could answer questions about the show and unlock extra video content.
The tech giant wouldn't reveal precise viewing figures, saying only that millions tuned in on the show's opening weekend.
A spokeswoman told Campaign that Amazon "never" reveals viewing or subscription figures for Amazon Prime, even to the production team.
Last week the show's producer, Andy Wilman, said the team would measure the first episode's success by what viewers tweeted.