Born on April 4, 1967 in Leningrad. His father's parents moved to Turkmenistan from Iran after World War I, fleeing hunger. On the way to the foreign land everyone starved, including Dmitry's grandfather Gulam, who was then 9 years old. He was placed in a Turkmen orphanage, where he was given an Azerbaijani surname. The grandfather, besides Russian, also spoke Arabic and Turkmen. Gulam's (Nikolai's) wife, Nagiev's grandmother Gertrude Sopke, was half German and half Latvian. Her ancestors were Balts with the surname Leie and Germans with the surname Sopke. The grandfather on his mother's side was the first secretary of the Petrograd district committee of the CPSU.

In his programs Dmitry Nagiev often mentions his grandfather, quoting his phrases (or attributing his own to him). He calls himself Russian: "I consider myself a Russian Orthodox person." In his youth Dmitry practiced sambo and artistic gymnastics, and back in the 1980s won the title of USSR champion among juniors. He was involved in black-market trading, for which he was subject to criminal prosecution. He is a fan of the St. Petersburg club Zenit.