The serving member of the elite unit was reportedly on a training mission with Kenyan Special Forces when the attack was launched.
At least four terrorists were involved in the slaughter at the Riverside hotel and office complex in Nairobi yesterday.
The attack killed 14, including one British man and an American woman, while another Brit is amongst the wounded.
The soldier is said to have taken part in the rescue mission with US Navy Seals.
Pictures and video from the scene show the Special Forces hero in jeans and body armour, holding a gun, as he escorts bystanders to safety.
The weapon he is clutching is a Diemaco C8 Carbine – standard issue for Special Forces soldiers.
A source told The Sun: “UK Special Forces always run towards the sound of gunfire.
“During the operation he fired off some rounds – its safe bet he hit his target – the SAS don’t miss.
“He is a long serving member of the Regiment, there is no doubt his actions saved lives.”
Islamist group al-Shabaab, which has links to al-Qaeda, later said it was behind the killings.
The Foreign Office said today it was supporting the family of a man killed in the attack.
A spokesman added; we are also supporting a British person who was wounded during the attack and is receiving medical attention.
“We stand ready to help any other British people affected.”
Chilling CCTV earlier showed four terrorists armed with guns and grenades during the attack on the DusitD2 hotel.
The Riverside complex that housed the hotel is also the location of the offices of a number of international businesses.
One of the victims was said to be an employee of LG Electronics.
Other firms based there include Colgate Palmolive, Reckitt Benckiser, Pernod Ricard, Dow Chemical and SAP.
The attack started yesterday afternoon came to an end overnight, with all of the militants reportedly killed.
Police are now said to have cordoned off an estate where one of the suspected terrorists lived.
As the attack unfolded witnesses were spotted covered in blood and fleeing for their lives.
Many survivors told Reuters news agency they had to leave colleagues behind, still huddled under their desks.
Office worker Simon Crump told the AFP news agency he had barricaded himself inside.
He said: “We have no idea what is happening. Gunshots are coming from multiple directions.”
The Ministry of Defence does not comment on Special Forces operations.