Smith, 41, led the BBC sci-fi series from 2010 to 2013 as the 11th incarnation of the Doctor, while Gatwa is the 15th and latest star to take on the role.
“I always keep my eye on Doctor Who. I think [Ncuti’s] great, he’s totally made for it,” Smith said on the BBC Radio 4 Today Programme on Wednesday (7 February).
“I dropped him a line and said ‘well done’,” the Crown star added.
Smith has previously praised the decision to cast Gatwa as the 14th Time Lord, telling Variety in 2022: “I think it’s the most sensational bit of casting. What an actor – he’s brilliant in Sex Education.
“I think he’s got something ‘other’ that that part really needs.”
Elsewhere on the Radio 4 interview, Smith admitted he “doesn’t really watch” The Crown since he left the show, which concluded on Netflix late last year.
“I have not kept up to date with it but I’m proud to be part of it,” he added.
Smith played Prince Philip in the first two seasons of the Netflix historical drama from 2016, with Queen Elizabeth II portrayed by Claire Foy. He was replaced by Tobias Menzies for seasons three and four, with Jonathan Pryce playing the royal consort in seasons five and six.
The Barbie actor recalled Whittaker telling him to “embrace the madness” of the experience in a conversation with Empire. “Thank God for that call on that day,” he noted, “because it was such a huge day for me, and they just wrapped me up in warmth like a welcome blanket.”
Peter Capaldi, who played the 12th Doctor, also praised Gatwa in a 2022 interview with STV.
“What a great story – a little boy whose family escaped from the genocide in Rwanda in 1994 and at age two, finds refuge in Scotland, where he grows up to become Doctor Who.
“That’s a story to be proud [of]. With his huge talent and heart, I know Ncuti will make an amazing Doctor. How exciting.”
Gatwa made his debut as the doctor on 9 December last year in a twist that few were expecting.
During the episode titled “The Giggle”, Gatwa is introduced as the new Doctor in what was expected to be David Tennant’s last appearance.
In previous years, when the Doctor transforms into their new form, the previous actor is killed off. However, Tennant underwent a “bi-regeneration”. Rather than the one Doctor transforming into a different character and allowing a new actor to take up the role, the Tennant incarnation of the Doctor was split into two different entities.
Tennant’s Doctor will remain alive and the new series will follow Gatwa on his adventures.