Guy Jack and Edward Legei were looking for souvenirs and gifts in the host city with team coach Shoaib Vayani when they bumped into Blair.
"We were browsing in one corner of the shop when the British Prime Minister Tony Blair walked in, came straight up to us and struck up a conversation," said Vayani.
"In our part of the world, a senior politician would have an entourage of at least 50 security guards - we didn't expect him to be so open and easy-going about meeting us."
The Kenyan pair are competing in the shooting competition, which gets under way in Bisley in the south of England on Saturday.
Blair, who was visiting Manchester before heading off to watch the opening ceremony on Thursday, asked the Kenyans how things were going in Bisley.
"After we told him Bisley was not due to start until Saturday, the Prime Minister said that he thought events there had already begun," Vayani added.
Jack is competing in the individual skeet event, while Legei is taking part in the full bore rifle event.