He takes the job only four months after he was sacked as coach of Tunisian club Esperance, following a disappointing start to their African Champions League group phase.
Krol has worked extensively across Africa, having held positions in Egypt, South Africa and Tunisia.
He is expected to join up with the 11-time Libyan champions on 1 November.
"It came out of the blue," Krol told Voetbal International in his native Netherlands.
"I have an idea of what I have to deal with. We have seven Libya internationals, who have all done well in Africa [in the CHAN] and the squad consists of forty men.