The 22-year-old enjoyed a solid 2019/20 campaign despite the Cherries' eventual relegation, making the third most saves in the Premier League.
United initially had a £12m bid turned down with Bournemouth eventually accepting an £18.5m offer earlier this month. Sky Sports have reported that Ramsdale began his Blades medical on Wednesday.
The Stoke-on-Trent born stopper joined the Cherries back in 2017 for around £1m and initially found first team opportunities hard to come by. He was shipped out on loan to Chesterfield and AFC Wimbledon before breaking into the senior set-up last season.
Ramsdale made his debut on the opening day and soon made the number one jersey his own, only missing one game during the entire campaign and keeping five clean sheets.Ramsdale came through the youth system at Bramall Lane and will be replacing Dean Henderson - who has returned to Manchester United following his loan move - at his boyhood club next season. Henderson was one of Chris Wilder's top performers last season, keeping 13 clean sheets, registering the third best save percentage in the division and earning a nomination for Premier League Young Player of the Year.
Ramsdale will soon become the latest in a growing list of high profile departures at the Vitality Stadium this summer. Long serving manager Eddie Howe has been replaced by former number two Jason Tindall, while club icons Andrew Surman and Simon Francis have both been released.
Despite Tindall's insistence that there would be no fire sale of the Cherries' playing assets, Nathan Ake has already packed his bags to join Manchester City. Meanwhile, David Brooks, Callum Wilson and Joshua King are also being strongly linked with moves away from the club.
Source : 90min