The head of the FSB security service, Nikolai Patrushev, said Basayev was killed overnight in Ingushetia, which borders Chechnya.
Chechen seperatists confirmed that Basayev had been killed, but said the rebel leader died while loading a truck with explosives.
Russian state television said residents of the village of Ekazhevo heard the blast as they watched the climax of the football World Cup final early on Monday.
"There was an enormous explosion. All those who were in a radius of the blast were blown to pieces," said Beslan Khamkhoyev of Ingushetia's interior ministry.
Basayev had claimed responsibility for numerous attacks, including the Beslan school siege in 2004, during which 331 people died, about half of them children.
Vladimir Putin, the Russian president, said on Monday that Basayev's death was "deserved retribution" for his actions.
"This is deserved retribution against the bandits for our children in Beslan... for all these acts of terror they committed in Moscow and other Russian regions, including Ingushetia and Chechnya."
The FSB said Basayev had been planning an attack to coincide with the G8 summit, which is due to be held in St Petersburg this week.
Basayev, in a television interview broadcast last year, justified the attack on Beslan by saying Russian civilians - including children - were legitimate targets in Chechyna's fight for independence from Moscow.
"We are at war. Russians ... pay their taxes for this war, send their soldiers to this war, their priests sprinkle holy water on the soldiers," Basayev said in the interview with Britain's Channel 4.