The Blades have forked out £18.5m for the 22-year-old’s signature, and he has signed a four-year contract at Bramall Lane.
Ramsdale previously spent four years with Sheffield United in the early stages of his career before getting sold to Bournemouth in January 2017.
Ramsdale played 37 times for relegated Bournemouth in the Premier League last season and was named as their player of the season.
He will be Chris Wilder’s first choice goalkeeper next season after Dean Henderson returned to Manchester United.
"I'm very fortunate to be able to come back to a place I call home and I'm just excited to get going, see the lads I left behind and meet the new ones now in the team," Ramsdale told the club's website.
"I'm delighted, it wasn't an easy decision to leave Bournemouth, but when a club comes in for you, shows that faith it has and is willing to pay this sort of money then obviously I've got to do a lot to repay it, but my smile has been ear-to-ear since I walked back through the door."
Wilder added: "The goalkeeping situation is something we have to make sure we get right."
"This is not about Dean, it's about bringing Aaron in, but Dean was outstanding for us for two years. We know a lot about Aaron, we've watched him develop on loan at Chesterfield and then AFC Wimbledon and obviously we've watched him this season too.
"I'd like to thank the board for their backing given the situation. Aaron is certainly amongst the best young goalkeepers in this country and we are delighted to have him."
