Expressing condolences, President Vladimir Putin called him an experienced and competent commander, a man of great courage, a true patriot.
The circumstances of his death are not clear. He became GRU chief in 2011.
In 2014 he was placed on EU and US sanctions lists targeting top Russian officials after Russia`s annexation of Crimea, in southern Ukraine.
The EU list said Gen Sergun was "responsible for the activity of GRU officers in eastern Ukraine". Gen Sergun is not thought to have had direct combat experience when he took charge of the GRU.
After graduating from military academies, he joined the service in 1984, and had various posts before working as military attache in Albania in 1998.
The GRU`s intelligence-gathering role dates back to the Cold War, when its officers were posted to Soviet embassies, along with KGB spies.
Ukraine role
Western analysts say the GRU played a key role in the seizure of Crimea and the insurgency by pro-Russian rebels in eastern Ukraine, which followed the Crimea annexation in March 2014.
Moscow denies that regular Russian troops have had a direct role in the Ukraine conflict, but last month President Putin said Russia could have people there "carrying out certain tasks including in the military sphere".
A top Russian commander in eastern Ukraine in 2014 - Igor Girkin, alias Strelkov - was identified as a GRU operative by the EU, which included him on the sanctions list.
According to Mark Galeotti, an expert on Russian security issues, the GRU recovered some of its former prestige under Gen Sergun, who took charge after some drastic cuts to the service.
The Kremlin sees GRU covert action as an asset again, after years in which the GRU`s role was downgraded, he wrote in Foreign Policy in 2014.
Russian GRU military spy chief Igor Sergun dies
05 January 2016
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The head of Russia`s secretive GRU military intelligence service, Gen Igor Sergun, died suddenly aged 58.
