Sadulayev was killed on Saturday by the regional police force in his hometown of Argun, 15km east of the provincial capital Grozny, the press service of Ramzan Kadyrov, the Moscow-backed Chechen prime minister, said.
The Interfax news agency quoted Muslim Khuchiyev, a minister in the local administration, as saying that police, acting on a tip, tracked down Sadulayev and killed him when he resisted.
Sadulayev had succeeded Chechen rebel leader Aslan Maskhadov, who was killed by Russian forces last year.
Top rebel aide Ibrahim Mezhidov confirmed on Saturday that Sadulayev was killed, according to the Kavkaz Centre website sympathetic to the rebels.
On the same day, speaking to Ekho Moskvy radio, rebel envoy Akhmed Zakayev, who lives in London, denounced Sadulayev's killing as a "political murder". He said Muslim commander Doku Umarov would now become secessionist president.
Sadulayev had been planning a terror attack in Argun to coincide with the Group of Eight summit of leading industrialised nations in St Petersburg in mid-July, Kadyrov said.
Wearing combat fatigues, Kadyrov posed for TV cameras next to a half-naked bloodied body identified as Sadulayev. He said a close associate of the rebel leader tipped police to his whereabouts for the equivalent of $55.
"He urgently needed to buy a dose of heroin, so he sold his leader for heroin," Kadyrov, flanked by his lieutenants, said with a grin.
Kadyrov (R) enjoys Moscow's
backing as Chechnya's premier
Kadyrov said his paramilitary police had wanted to capture Sadulayev but had to kill him when he resisted arrest.
Russian television stations showed the basement of a house where the rebel leader was allegedly hiding, its wall riddled with bullets.
An intelligence agent and a police officer were killed in the operation, the Federal Security Service, the main KGB successor agency, said in a statement.
One rebel also was killed and two rebels escaped, NTV news reported.
Sadulayev's killing, if confirmed, would be a further evidence that the rebels' position is weakening in Chechnya even as Islamic-inspired fighters have spread their influence across the volatile North Caucasus region.
Russian news agencies quoted Kadyrov as saying: "The terrorists have been virtually beheaded. They have sustained a severe blow, and they are never going to recover from it.
A handout picture of Sadulayev,
who once was a Sharia judge
"We must decisively end international terrorism in the whole of the North Caucasus."
Sadulayev, a fundamentalist field commander, was relatively unknown outside rebel circles.
He had served as a judge of the Chechen rebels' Sharia committee - an extension of the Islamic court established under Maskhadov when he was Chechnya's elected president in the 1990s.
Sadulayev had promoted efforts to spread the rebel movement beyond Chechnya's borders in the so-called Caucasus Front and attack Russian forces across the poverty-stricken and corruption-gripped south.