The popular actor, who previously appeared in an episode of the hit sci-fi series when the Time Lord was played by Matt Smith, tells HuffPostUK:
"I think it's one of those things you read and you think, 'Well, of course Peter Capaldi is going to be Doctor Who, it makes perfect sense.'
"He's a wonderful actor, and I would think he'll be a terrific doctor.
"He'll be very funny, dry, elegant and sharp, and I think it makes perfect sense."
Bill Nighy appeared as the mysterious Doctor Black in 'Vincent and the Doctor' with Matt Smith
Nighy previously revealed that he had once been offered the role of the Time Lord himself, but had turned it down.
However, Nighy has appeared in the series. He played art gallery curator Dr Black in 'Vincent and the Doctor', broadcast in 2010, which saw Doctor Who travelling back in time to meet tragic artist Vincent Van Gogh, who believes he can see a monster invisible to everyone around him.
Nighy was uncredited in the role, but the episode was written by Richard Curtis, in whose films the actor has frequently appeared.
And following the theme, Nighy stars in Curtis's next film 'About Time', starring Domhnall Gleeson and Rachel McAdams, which also features time travel as its central theme.
'About Time', which is in UK cinemas from 4 September, sees Tim (Gleeson) told by his father (Nighy) that all the men in the family share a secret - that they can travel back in time to another occasion in their lifetime, should they wish to change its outcome. This power turns out to be more complicated to accommodate than it would at first appear.
Capaldi was named the 12th Doctor Who on Sunday evening, live on television, when he admitted that it was great "not to have to keep the secret any longer".
Staying on Doctor Who, Ebay.co.uk have reported that sales of Doctor Who memorabilia have soared on their auction site since the new doctor was announced. According to their records, sales of souvenirs relating to Matt Smith have increased by 80%, but he remains in second place, behind the most popular Time Lord of all, when it comes to merchandise - Capaldi's fellow Scot, David Tennant.