The Blades, who have confirmed a final friendly of pre-season against French club Stade de Reims on August 3, are gearing up for a first campaign back in the Premier League for 12 years.
Nottingham Forest midfielder Osborn was the first to seal his switch to Bramall Lane today, closely followed by Manchester United goalkeeper Henderson.
The latter has returned on loan after being an ever-present in the club's promotion winning campaign. Henderson, seen as a potential number 1 at Old Trafford in the future, signed a new deal with the Red Devils before agreeing the switch to south Yorkshire.
“I am looking forward to being back at Bramall Lane," he said. "The opportunity to be reunited with the coaches and play in front of the amazing fans again is one that I am relishing. I cannot wait to enjoy a full season of Premier League football which I know will be hugely beneficial for my career.”
Osborn, meanwhile, has signed a three year contract at Bramall Lane. "We are delighted that he is a Sheffield United player," said United manager Chris Wilder, who has targeted hungry players during a summer that has also seen him raid the Championship to sign Luke Freeman and Callum Robinson for a combined £12m.
"He has been a fantastic player for Forest in the Championship and I know for certain that two or three clubs in January were sniffing around to take him. He has got a lot of attributes that will help us, going forward, and we are looking forward to him pulling on a red and white shirt.
"Ben is an intelligent footballer, he plays a number of positions and has got that attitude that he will slot in wherever.
"But he will want to nail down a position and he is going to put enormous pressure on a few of our players who might think they are cemented into the team. That is how it has got to be, I have said that all along.
"It raises everyone's standards. We are putting together a group that has got to be competitive in arguably the best division in the world.
"We are not getting flustered with people talking about where we are getting our players from, we are delighted with the work we have done. I am really excited at seeing the players we have got in the building already, from Jags (Phil Jagielka) to the likes of Ravel (Morrison), Lys Mousset, Callum Robinson, Luke Freeman and now Ben Osborn."