In a message posted on a Web site known to carry messages from Chechen rebels, Umarov said he ordered the attack in which 36 people died and scores were wounded, CNN reported Tuesday.
"The special operation was done in accordance with my order. Similar special operations will be taking place in the future," he said in a message posted Monday on the pro-insurgent Kavkaz Center Web site.
In another message posted during the weekend, Umarov said he would bring "a year of blood and tears" to Russia, saying dozens of rebels were prepared to undertake attacks.
"I won't tell you there are hundreds of us prepared for jihad. But 50 or 60, God willing, we will find," Umarov said in the weekend post. "Those operations will be conducted monthly or weekly, as Allah allows us."
In Moscow, investigators said they identified the suspected bomber in the Jan. 24 Moscow Domodedovo International Airport as a 20-year-old man from the North Caucasus region.
Alexander Bortnikov, the head of Russia's Federal Security Service, said the alleged bomber had drugs in his system.
"Biological studies revealed the presence of a huge amount of highly potent narcotic and psychotropic substances in parts of the suicide bomber's body," Bortnikov said.
Since the attack, a government official said a number of senior Russian intelligence service officials have been fired, RIA Novosti reported.
A Federal Security Service source confirmed a shake-up, but said anti-terrorism department heads "continue working in their posts."
2014: The Year in Music [PHOTOS]