Harris takes over from Brian Noble, who was told last week that he would be replaced by the 37-year-old Welshman.
Noble suggested over the weekend that he was receiving legal advice following the surprise shake-up.
The former Great Britain coach, who was expected to recruit Harris as part of his backroom staff, has been offered a directorial role at the AJ Bell Stadium.
"Iestyn started work in earnest this morning," chief executive Martin Vickers is quoted as saying by Sky Sports News. "Along with (chairman) Marwan Koukash, he addressed the whole squad before the start of training."
Harris is also the coach of the Welsh national team.