Petev, who signed a contract until the end of the 2014-15 season, hit the headlines earlier this month, when he left 26-times Bulgarian champions Levski Sofia only a day after being undressed and forced out of his first news conference.
The 38-year-old is considered one of the best young coaches in Bulgaria after leading Ludogorets to back-to-back league titles. He was sacked by Ludogorets after a surprising defeat in the opening round of the domestic championship.
AEL are fourth in the Cypriot league with 11 points from six matches, four points behind leaders Anorthosis Famagusta and Angolan coach Vidigal was criticised for the team's mediocre performances.
Last year, AEL won their sixth league title and reached the Champions League's group stage after knocking out Linfield, Partizan Belgrade and Anderlecht in the preliminary rounds.