The relaunched programme drew in an average of 5.1 million viewers on Saturday night and enjoyed an audience share of 30 per cent for its timeslot.
The programme reached a peak of 5.7 million viewers during its broadcast from 9.15pm until 10.20pm, ITV said.
BBC One’s Casualty, also on at 9.15pm, had an average of 3.4 million viewers.
However, despite the success of Millionaire - it was more than one million up on viewers compared to the timeslot’s year-to-date average - it was still beaten in the ratings by ITV’s Britain’s Got Talent.
The fourth episode of the TV talent show, hosted by Ant and Dec, was the most-watched of the night across all channels, with an average of seven million and a peak of 8.2 million viewers.
Former Top Gear star Clarkson is in the hot-seat for a special seven-episode run of programmes to mark Millionaire’s 20th anniversary, taking over from original host Chris Tarrant.
His debut was largely hailed a success by viewers, although the contestants hoping to win big money prizes were not so lucky.
The Grand Tour presenter littered his performance with a number of quips, attempts at the Scottish and Yorkshire accents, took aim at his co-star Richard Hammond’s reputation for crashing and referenced the show’s coughing scandal.
Clarkson came under fire recently after he urged Scots to forget about indpendence.
The presenter made the comment after he spent a week filming in Scotland with colleagues Richard Hammond and James May for their Amazon Prime series The Grand Tour.
The former Top Gear host, 58, told how his trip had turned his thoughts to the independence debate and insisted the country should not go to the polls again.
He said independence was not the top priority for the locals he met and getting rid of the English would not “unite the country and bring back Sean Connery”.