The 18 year-old striker joins the Millers today after talks with boss Steve Evans to seal a switch to the New York Stadium.
Morgan, a left footed product of the Anfield youth academy, has featured three times in the Reds Europa League campaign this season.
He could make his Millers debut in the FA Cup clash at Aldershot on Saturday subject to paperwork going through in time.
"I am delighted with the signing, a lot of hard work has taken place to get this young lad to the club. I will have more to say when formal registration process has been completed," Evans told www.themillers.co.uk
More to follow tomorrow.