Akhbari, 35, was without a team since parting company with Machine Sazi in February.
Faraz Kamalvand, who had been named as Saipa coach three months ago, stepped down from his role on Saturday.
Akhbari has a tough task to help Saipa avoid relegation since it sits 15th in the 16-team table.
Saipa is scheduled to meet Gol Gohar on Tuesday.