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The Home Office ruled that the player had not made sufficient appearances for the American international side over the past two years.
Manager Steve Bruce and club secretary Alan Jones attended a review by Work Permit UK in Sheffield and argued mitigating circumstances on the player's behalf and Work Permit UK agreed to overturn the original decision.
Kirovski has already agreed personal terms and passed a medical and could now be signed up in time for Blues first game of the season against Arsenal on Sunday.
Club secretary Alan Jones told the club's official website: "We're absolutely delighted with the decision and as long as the relevant paperwork comes through within the next 24 hours, we hope to have Jovan registered by the weekend.
"If that is the case there is every chance that he will be available for selection for the trip to Highbury."