Houston worked under Levein during his spell at Hearts whilst Black had been caoching at Airdrie.
"We are in the middle of trying to put a team together off the field, first and foremost. I think it is important for me to get my own people in as quickly as possible, the new Foxes boss told the clubs official website on Monday.
"So far we have brought in Peter Houston and Kenny Black. I know Peter very well having worked closely with him at Hearts, while I played with Kenny at Tynecastle.
"After we have sorted that side of things out we can then look at the players and gain experience and knowledge of them."