The 23-year-old was due to return to his parent club upon the expiry of his temporary deal on 30 June, but he will now remain at Bramall Lane until the conclusion of the 2019/20 Premier League campaign.
Henderson has excelled during his maiden season in the top-flight, keeping 11 clean sheets and featuring in all but two of the Blades' games as they seek to secure European football for the first time in their history.
Due to Premier League rules around playing against parent clubs, Dean was ineligible for the fixtures against United - a 3-3 draw at Bramall Lane in November, and last week's 3-0 victory at Old Trafford.