Takagi was born in Aomori City in Aomori Prefecture in northern Japan. He graduated from the Daiichi High School (which was often abbreviated to Ichi-ko) and Kyoto Imperial University, where he studied metallurgy. He was employed by the Nakajima Aircraft Company, but lost his job with the prohibition on military industries in Japan after World War II.
On the recommendation of a fortune-teller, he decided to become a writer. He sent the second draft of his first detective story, The Tattoo Murder Case, to the great mystery writer Edogawa Ranpo, who recognized his skill and who recommended it to a publisher. It was published in 1948.
He received the Tantei sakka club sho (Mystery Writer Club Award) for his second novel, the Noh Mask Murder Case in 1950.
Takagi was a self-taught legal expert and the heroes in most of his books were usually prosecutors or police detectives, although the protagonist in his first stories was Kyosuke Kamizu, an assistant professor at Tokyo University.
Takagi explored variations on the detective novel in the 1960s, including historical mysteries, picaresque novels, legal mysteries, economic crime stories, and science fiction alternate history.
In The Informer (1965), a former Tokyo stock exchange worker who is fired because of illegal trades. A subsequent stock market crash means that he has no hope of returning to his old career and therefore he accepts a job from an old friend even though he eventually discovers that the new firm he works for is really an agency for industrial espionage. The plot is based on actual events.
He was struck by stroke several times since 1979, and died in 1995.