Lebed (l) with former Russian President Boris Yeltsin
The Mi-8 helicopter is said to have hit a power line in poor weather conditions at 0615 local time before crashing near Abakan, about 2,100 miles (3,400km) east of Moscow.
Lebed, elected governor of the huge Krasnoyarsk region in 1998 and once a prominent army general, was taken to a nearby hospital with severe injuries but later died.
At least five other people were killed in the crash.
He and other local officials were on their way to open a new ski centre in the district of Yermakovskoye.
Popular figure
Russian President Vladimir Putin has sent his condolences to Lebed's family.
A commission to investigate the crash, headed by Emergency Situations Minister Sergei Shoigu, has also been set up, Russian news agency Interfax reported.
Lebed, 52, who came third in the Russian presidential election of 1996, was once considered a possible successor to President Boris Yeltsin.
He was widely credited with ending Russia's 1994-96 campaign in Chechnya, and was a popular figure with the Russian people.
He trained as a paratrooper before rising through the military ranks to become battalion commander during the Soviet military campaign in Afghanistan from 1981-82.
He won plaudits for his action during the attempted August 1991 coup against then Soviet President Mikhail Gorbachev, when he refused to deploy his troops against coup opponents.
After resigning in 1995 from the army he unsuccessfully ran for the Russian presidency.
However, following his election as governor to Siberia's Krasnoyarsk region, some had hoped he would run again, but he declined.