The former Scotland and Everton defender leaves his coaching job at Goodison Park to take over at Bramall Lane on a three-year contract, succeeding Danny Wilson
The former Everton defender succeeds Danny Wilson, who was sacked in April following a poor run of results.
Weir has signed a three-year deal to take over at Bramall Lane and has been tasked with the challenge of getting the club out of League One.
Weir, a former coach at Goodison Park, was among the candidates for the manager's job at Everton prior to the appointment of Roberto Martinez, Goal understands.
“My first thoughts about the job are of excitement. I understand how privileged I am to be named manager here," he told the club's official website.
“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."