After her first episode, the consensus among fans on social media seemed to be that she is right for the part.
Comments ranged from "A breath of fresh air" to "This is everything the show was ever meant to be" and "Jodie has nailed it at the first attempt".
With Whittaker taking over from Peter Capaldi, the show has moved to Sundays.
The West Yorkshire-born former Broadchurch actress was wearing Capaldi's outfit for most of the episode, and addressed her status as the first female Doctor early on.
When someone told her she was a woman, she replied: "Am I? Does it suit me? Oh yeah, I remember. Half an hour ago I was a white-haired Scotsman."
There was also a thinly-veiled message to any sceptical fans when her character said at one point: "Don't be scared. All this is new to you and new can be scary."
After the first episode, it was also announced that this series will feature guest performances from Alan Cumming, Chris Noth, Mark Addy, Julie Hesmondhalgh and Lee Mack.