The committee says the suspect was recruited by Ukrainian intelligence services and was paid $100,000 (£79,000).
The senior general was killed on Tuesday by a bomb hidden in an electric scooter outside an apartment block in Moscow, a day after Ukraine’s security service brought criminal charges against him.
A Ukrainian official said the service carried out the attack.
The general’s assistant also died in the explosion.
Dashcam footage at the scene captured the moment the bomb detonated on the street as the two men walked out of the building about 4 miles (7km) southeast of the Kremlin.
The committee said that under interrogation, the suspect admitted he had been recruited by Kyiv, who supplied him with a homemade bomb after he arrived in the Russian capital.
He placed the device on an electric scooter, which he parked at the entrance to General Kirillov’s home, monitoring the scene via a surveillance camera installed in a hire car.
Footage from the camera was watched by “the organisers of the terrorist attack in the city of Dnepr”, the committee said.
“After a video signal was received about the soldiers leaving the entrance, the explosive device was remotely activated by them.”
As well as the money, the man was offered the chance to move to Europe in return for his part in the assassination, the committee said.
Photographs posted on Russian Telegram channels showed two bodies lying in the blood-stained snow next to the wrecked entrance to a building.
Russian news agency TASS said the bomb contained the equivalent of 300g of high explosive.
Several cars and the first four floors of the apartment building were damaged, the news agency added.
Russia’s radioactive, chemical and biological defence soldiers, known as RKhBZ, are special forces who operate when there is a threat from radioactive, chemical and biological contamination.
On Monday, a Ukrainian prosecutor opened a case against General Kirillov in absentia, accusing him of using banned chemical weapons in Ukraine, the Security Service of Ukraine said.
It was claimed that General Kirillov was “using dangerous chemicals mainly in the hottest areas of combat, where they [Russia] are trying to hide the use of chemical agents under dense artillery fire”.
Russia denies those accusations.
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The e-scooter, which Sky News’ Data and Forensics team has geolocated to the scene outside a residential building in Moscow, is from KugooKirin.
The brand was founded in China but has multiple overseas warehouses across Europe, including in Russia.
Russia is also one of its main exporting countries, according to the company’s website.
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