James Thomas, 57, was in a supermarket in the Westgate Mall when gunmen reportedly belonging to Somalian Muslim extremist group Al-Shabaab started shooting shoppers at random.
St Peter's Church, Mowbray, where he was a warden, confirmed that Thomas had died of a gunshot wound.
Pastor David Meldrum was quoted by The Times Live as saying Thomas's wife, two children and foster son were "in shock".
"He was an extreme extrovert, fun-loving, a people's person who liked to see the best in others to help them develop their potential," said Meldrum.
"He wanted people to be the best they could be. He could not tolerate unemployment for himself or for others and wanted people to find their purpose and their calling.
''He had a real vision to see people, through their own potential and ability, work their way to something better."
At least 62 people have been killed and over 170 injured since the attack started on Saturday.
Smoke was billowing at the mall today after blasts were heard. According to the BBC, security forces have launched an assault to break the grip of the militants and rescue remaining hostages.
Three Britons are among the dead. Victims also include Ghanaian poet Kofi Awoonor, 78, and President Uhuru Kenyatta's nephew, Mbugua Mwangi and fiancee Rosemary Wahito.
The Anglican Communion Office said it was praying for an end to the hostage crisis.