The disgraced health professional was convicted of killing seven babies and trying to kill six more in a case that has horrified people across the country.
The review was ordered after Letby was found guilty and given a whole-life sentence earlier this month.
Health Secretary Steve Barcely said he had listened to the families and was now giving the inquiry far-reaching powers.
He said he “respects the wishes” of the families and decided that this was the best way forward for the Lucy Letby Inquiry.
He added: “My priority is to ensure the families get the answers they deserve and people are held to account where they need to be.”
He also said that the decision on who would chair the inquiry would be made in the coming days.
Of the move, Richard Scorer, a lawyer representing two of the families affected by Letby’s crimes, said: “We’ve always said we wanted an effective inquiry – an inquiry capable of compelling people to give evidence under oath and to compel the production of documents.
“It looks like we’ve got the statutory inquiry we need and that is really important.”
This comes after the 33-year-old former nurse refused to appear in court for the sentencing hearing.