Midfielder Reed has put pen to paper on a new deal which will be triggered when he celebrates his 18th on Saturday.
“Louis is another homegrown player and his new contract is another sign of how we appreciate the work that goes on at our academy at Shirecliffe,” Blades boss Nigel Adkins told the club’s official website.
“He played a good amount of games last season and was recognised at his age group level by England.
“But Louis is a well-grounded lad and knows that there is plenty of hard work ahead of him as he bids to build a successful football career.”
Reed became United’s youngest-ever League player in April 2014 when he made his debut off the bench against Rotherham aged 16 years and 257 days and last season made a total of 32 appearances.