Ajax recruited the left-footed playmaker in December after he impressed on a trial in Parow.
“Kabwe is a brilliant number 10, who scores and creates goals,” Efstathiou told his club's website.
“He netted 10 goals for Zanaco last season and will be a tremendous asset to the club. He is a class player.”
The 24-year-old Chipolopolo international will compete for game-time at the Urban Warriors with the likes of Mark Mayambela and Bantu Mzwakali.
Ajax, in ninth spot on the table, return to training on Tuesday, and will resume their campaign against joint-log leaders Bidvest Wits at Bidvest Stadium on February 7.