The former Rangers and Everton defender, 43, who had been working as a coach at Goodison Park after retiring as a player in 2012, has signed a three-year deal to take on his first managerial role.
Weir replaces Danny Wilson, sacked in April with five games of the regular season remaining, and becomes the Blades' seventh permanent manager in the last seven years.
Weir told the club website: "My first thoughts about the job are of excitement, I understand how privileged I am to be named manager of a fantastic football club like Sheffield United.
"I realise what a great opportunity is in front of me now and my message to the supporters is that I will work hard and give everything to be successful at Bramall Lane.
"I honestly can't wait to get started and get a real feel for the club, then obviously I am eager to get organised for when the players return for pre-season training later this month."
Chief executive Julian Winter said: "We are thrilled to appoint David and the three-year contract emphasises the fact that he will assist in a change in club culture. I have stated before that the club needs to act differently and David is young, has a great pedigree and will bring a new vision and leadership to the club.
"The process of appointing a new manager has taken slightly longer than we envisaged but by taking our time we believe we have the attracted the right man to take Sheffield United forward."
Weir, who began his playing career at Falkirk before a three-year spell at Hearts, moved south of the border to join Everton in 1999 and went on to make over 230 appearances for the Merseysiders.
He returned to Scotland in 2007 with Rangers, where he made over 140 appearances in five years before announcing he wanted to extend his playing career back in England. Weir trained briefly with the Blades, but instead returned to Everton in early 2012 to join the club's coaching staff.
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- Sheffield United