The new deal will come into effect on Saturday, when Reed turns 18.
Reed is the youngest player to appear for the Blades in a league game, having made his debut against Rotherham aged 16 years and 257 days, and made 32 appearances last season.
He told the League One club's website: "Being in and around the first team all last season was a great learning experience for me."
Sheffield United midfielder Louis Reed has signed a new three-year contract.