The 'Thick Of It' star will also be an "older, trickier and fiercer" Doctor, Moffat told the hit BBC sci-fi show's official magazine, Doctor Who TV.
Capaldi was unveiled as the 12th Timelord in a live show earlier this month, after Matt Smith decided to leave the role behind.
"It's so wonderful not to keep this secret any longer," he said after he walked out on stage. "For a while, I couldn't tell my daughter, who kept looking on the internet, and was getting upset because they never mentioned me.
"I had to keep saying, 'Rise above it, darling.'"
He will replace Smith at the end of the year, during the show's Christmas special and Moffat said he made the decision to cast an older actor as a contrast to Smith and David Tennant.