In a video posted online, Mr Umarov said the attack was a response to "Russian crimes in the Caucasus".
Similar suicide attacks would continue, he added, speaking in Russian.
Mr Umarov is self-styled leader of the "Caucasus Emirate" and is considered the head of the Islamist militant insurgency in the North Caucasus. He is one of the few prominent Chechen rebels still active, having served as security minister in the Chechen separatist government from 1996-99.
Another video of the rebel leader was posted online late on Friday last week in which he threatened a year of "blood and tears" but made no explicit reference to the airport bombing.
Doku Umarov's claim that he ordered the Domodedovo bombing will not come as a surprise to Russians.
The Chechen warlord has been linked to previous acts of terror.
But his declaration that there are hundreds more suicide bombers ready to strike at any moment will spread fear across the country.
Following the Domodedovo bomb, the authorities have taken measures to prevent similar attacks.
As of 1 February, there are new security regulations at Russian airports. It means tighter controls outside airport buildings and more document checks.
One Russian newspaper this morning warned passengers to arrive four hours before a flight. It also predicted that it would be harder for individuals without valid air tickets to get access to the terminals.
What's more, a string of law enforcement officials have been sacked and a new head of transport security has been appointed in the Interior Ministry.
But few Russians believe that these measures will prevent future terror attacks and provide them security.
The Chechen warlord has been linked to previous acts of terror.
But his declaration that there are hundreds more suicide bombers ready to strike at any moment will spread fear across the country.
Following the Domodedovo bomb, the authorities have taken measures to prevent similar attacks.
As of 1 February, there are new security regulations at Russian airports. It means tighter controls outside airport buildings and more document checks.
One Russian newspaper this morning warned passengers to arrive four hours before a flight. It also predicted that it would be harder for individuals without valid air tickets to get access to the terminals.
What's more, a string of law enforcement officials have been sacked and a new head of transport security has been appointed in the Interior Ministry.
But few Russians believe that these measures will prevent future terror attacks and provide them security.
Doku Umarov has previously claimed the March 2010 suicide bombings on the Moscow Metro in which 39 people died, and is said to have ordered the November 2009 bombing of a train from Moscow to St Petersburg that left 26 dead.
'On my orders' The video which appeared on the Kavkaz Tsentr website is dated 24 January, the day of the attack.Appearing alone, dressed in combat fatigues, Mr Umarov speaks to the camera: "This special operation was carried out on my orders and, God willing, special operations like it will continue to be carried out."
He goes on to argue that Muslims are under attack all over the world, talking at length about the situation in Sudan, and condemns "Zionist and Christian regimes led by Israel and America".
Mr Umarov says that he and his fighters "are waging jihad in the Caucasus today to establish the word of Allah", and there are "hundreds more brothers" ready to sacrifice themselves to that end, in the fight with Russia's "racist regime".
Promising "regular, deeper and more aggressive operations", he says he wishes that so much blood did not have to be spilt for Russia to "leave the Caucasus".
'Special operation'
Doku Umarov was flanked by two men in an earlier video. The younger man (R) is named "Seifullah" Although the attacker has not been named officially, unnamed officials told the Interfax news agency on Sunday that he was believed to be Magomed Yevloyev from a village in Ingushetia in the northern Caucasus.
In the video of Doku Umarov posted last Friday, the rebel leader is flanked by two men, one of whom the rebel leader claims is preparing a "special operation". Russian media have suggested that the man in the video, named "Seifullah" by Mr Umarov, was Yevloyev.
At least seven foreigners were killed in the bombing at the airport - the busiest serving the Russian capital. The arrivals hall was full of people as several international flights had just landed.
Those killed included one person each from Britain, Germany, Austria, Ukraine, Tajikistan, Kyrgyzstan and Uzbekistan. At least 16 Russians were also among the dead.
Russian President Dmitry Medvedev sacked several officials - said to include a regional transport chief and a Moscow police deputy head - after the bombing, blaming them for poor security.
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