With nearly 85% of votes counted by 0400 GMT on Monday, Alkhanov, 47, handpicked by Russian President Vladimir Putin for the role, won nearly 74% of votes in Sunday's polls, more than enough for an outright victory.
The Itar-Tass news agency quoted Moscow's interim president of the republic, Sergei Abramov, as saying 80% of the electorate had turned out to cast a ballot - well over the 30% required to make the vote legitimate.
His nearest rival, Movsar Khamidov, received just 13.5% of the ballot, the electoral commission said.
Abd Allah Bugayev is currently in third place with 5.6%. The other four candidates collected less than 5% between them.
However, final results are not due to be announced until 0800 GMT on Monday.
The poll was forced when separatists assassinated Kremlin-backed president Akhmad Kadyrov in an explosion four months ago.
Questions remain about how so many could have voted when observers reported an almost total lack of activity at polling stations on Sunday, with the Russian press expressing incredulity.
"The name of the winner was known in advance. This as well as the threats of the rebels and the good weather meant Chechens lost any desire to go to the ballot box," said the daily Kommersant.
"The name of the winner was known in advance. This as well as the threats of the rebels and the good weather meant Chechens lost any desire to go to the ballot box"
Kommersant, Russian daily
Usam Baysayev, a representative of the rights group Memorial in neighbouring Ingushetia said that "in reality there had been no presidential election in Chechnya".
He said in the northern village of Mekenskaya no-one had voted before 0200pm on Sunday, but the authorities were still boasting a turnout of 35%.
"Whatever the voting slip that goes into the ballot box looks like, the candidate chosen by the Kremlin will be elected. And to the indifference of the international community," said a Chechen official with the pro-Russia administration.
No separatist talks
Security has been tight during
the voting process
Alkhanov has ruled out any possibility of talks with Chechen separatist leader Aslan Maskhadov.
"Maskhadov and Wahhabism have no future in Chechnya," Itar-Tass quoted Alkhanov as saying.
The separatists "may kill and make explosions, but the will of the people has thrown them into the dustbin of history and Maskhadov has chosen this way himself. The talk of the imaginary legitimacy of Maskhadov is misplaced," Alkhanov declared.
Maskhadov was elected Chechen president in 1997, after the republic won de facto independence from Russia, but has since been branded a "terrorist" by Putin.
Russia has been fighting separatists in the mainly Muslim northern Caucasus region of Chechnya since it first tried to break away in the 1990s.
Mashkhadov has been in hiding since Russian troops retook the capital Grozny in 1999, but resistance continues.