Pertwee - who is set to appear in the finale of BBC Sunday night drama The Musketeers alongside Capaldi this weekend - is the son of Jon Pertwee, the third actor to play the Time Lord in Doctor Who.
Pertwee revealed how much he enjoyed talking to Capaldi about the role of the Time Lord when they met on The Musketeers set.
He believes 55-year-old Capaldi will be "stupendous" as the centuries-old alien, following on from 31-year-old Matt Smith.
Pertwee said: "My father was very fond of Peter and Peter is an extremely lovely gentleman. He was very kind to my family when my father passed away."
"I think he's going to bring some real gravitas and weight, which only comes with age. Taking nothing away from Matt (Smith), who I thought was great, I just think he's going to have a completely different look.
"He's such a phenomenal actor anyway I think he'll be absolutely brilliant. I'm delighted he's doing it."
The final episode of The Musketeers, starring Hugo Speer, Tom Burke and airs on BBC One at 9pm on Sunday.