Henderson, who helped Chris Wilder's side reach the Premier League last term, returned to South Yorkshire on another season long loan after leaving Manchester United. Osborn, previously of Nottingham Forest, signed a three year contract following his departure from the City Ground.
"Dean was always our number one target," Wilder, the United manager said. "We've had to fight to get a good deal and that's part and parcel of our approach in the transfer market. All of us, from myself, to the coaching staff, to the player and the supporters want him playing for us in the Premier League and with a lot of hard work we've made that happen."
"We are delighted that he is a Sheffield United player," Wilder, announcing Osborn's arrival for an undisclosed sum, added. "He's 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's got a lot of attributes that will help us, going forward, and we're looking forward to him pulling on a red and white shirt."
Although negotiating Osborn's exit has been relatively simple -The Star revealed a deal had been agreed in principle a fortnight ago - securing Henderson's release proved anything despite the player's desire to rejoin United. However, after handing him a new long term deal, officials at Old Trafford sanctioned the 22-year-old's release ahead of tomorrow's friendly against Barnsley. Osborn, aged 24, could also feature at Oakwell.
Wilder, who is now expected to focus his efforts on prising Oli McBurnie away from Swansea City, has also unveiled Phil Jagielka, Lys Mousset, Callum Robinson, Ravel Morrison and Luke Freeman since guiding United back into the top-flight.
Wilder, whose squad will complete their preparations for the new campaign with a visit to Stade de Reims on August 3rd, said: "We're not getting flustered with people talking about where we are getting our players from, we're delighted with the work we've done, I'm really excited and seeing the players we've got in the building already."