The eight-day tournament will be played at the Nairobi Gymkhana club where the three countries will play each other twice before the final, Cricket Kenya (CK) chief Tom Tikolo told reporters.
Zimbabwe had earlier declined to take part in the triangular tournament, claiming its schedule was too busy to accommodate the series.
Zimbabwe recently retained its full membership in the International Cricket Council but agreed to pull out of the World Twenty20 championships in England as part of the deal.
Calls have risen in Kenya to ban the visitors in protest at President Robert Mugabe, who is accused by the Zimbabwean opposition of fixing elections earlier this year.
Kenya will be looking to bounce back from a dismal showing on their tour of Europe in August during which they failed to qualify for next year's Twenty20 World Chmapionships in England.