The show launched on the Amazon Prime streaming service on Thursday evening.
It is the first programme to be fronted by Clarkson, Richard Hammond and James May since they parted company with the BBC last year.
Writing in The Evening Standard, Ben Travis described it as a “stunningly beautiful show”.
“If The Grand Tour is basically Top Gear with a nitros boost of Amazon finances, the difference is immediately apparent,” he said.
“Those who have never counted themselves as Jeremy Clarkson fans aren’t exactly going to be won over here – but episode one is a confident opener that leaves the BBC’s attempted Top Gear revival in the dust.”
Writing in The Guardian, Sam Wollaston said: “More than format, more even than the amount of money you throw at something, what really gives a television show its personality is the personnel.
“You can pour something into a different container, but it still tastes the same. And, like it or not, this tastes of Clarkson, Hammond and May.”
He added: “Fans of old Top Gear are going to be happy.”
The first episode of the series saw the trio take their travelling studio tent to Dry Rabbit Lake in the Mojave Desert in California.
Vehicles featured in the episode included hybrid hyper-cars such as the McLaren P1, the Porsche 918 Spyder and the Ferrari LaFerrari.
The Telegraph’s Ed Power said: “The Grand Tour isn’t a shameless Top Gear rip-off. But under the hood the rival franchises have a great deal in common.”
He added: “The new series will certainly go some way towards obliterating memories of Top Gear’s terrible Chris Evans-fronted relaunch. Petrolheads can rejoice.
“The BBC may wonder how Matt LeBlanc and whoever joins him next year can possibly compete.”
Dan Wootton gave The Grand Tour five stars in his review for The Sun.
“Being sacked from the BBC was the greatest thing that ever happened to Clarkson and co – and the world of cars on TV,” he wrote.
Wootton said it has “guns, explosions, super yachts, madcap stunts, the British Institute of Car Chases, dramatic crashes, a sinking ship and Hammond being dangled from a chopper”.
He added: “But the one thing that really matters is Clarkson being reunited with his two mates on screen.”
Digital Spy’s Tom Eames said: “Clarkson, Hammond and May’s reunion is silly but worth the wait (and money).”
“It’s precisely all the things we loved about their old show, but bigger, brighter and more blow-upier.
“And they’ve sort of somehow come up with the world’s first scripted comedy factual show, and it works perfectly.”
The first series of The Grand Tour will consist of 12 hour-long episodes – with one being made available each week.
A total of 36 episodes across three years have been commissioned by Amazon.
Currently, only fans in the UK, America, Germany and Japan are able to watch the first episode, but the company has announced it will be launching the show globally in December.
The new series does not include features such as “star in a reasonably-priced car” or The Stig – as those belong to the BBC’s Top Gear format.
Matt LeBlanc and Chris Evans took over presenting duties on Top Gear after Clarkson, Hammond and May’s departure, although Evans left the show after one series.
Clarkson has previously said of the new show: “I think programme one will be all right. I’d be extremely surprised if that was poorly reviewed.”