The 23-year-old, who has scored 14 goals for the Blades this season, caught the eye of Royals manager Brian McDermott during Saturday's FA Cup tie between the two sides.
Blackman, whose fee is reportedly £1.2m, told Reading's official website: "I'm really looking forward to it and I'm very excited.
"I met the gaffer last night, he was fantastic with me and I couldn't have asked any more from him and Nicky Hammond. I can't wait to play - hopefully I can try and get involved as soon as possible."
McDermott added: "We're very pleased to get him. He had options elsewhere but he knows that we try to develop our players and get them better. He's played a lot of games, and has so much more to come.
"He can play in three or four positions - up front, either one of the wide areas and off the striker.
"He's another player that's hungry, wants to learn and wants to improve. His goalscoring record is getting better, better and better every year. He takes set plays, so he's a really good acquisition to the group."
Blackman started his career at Macclesfield before moving to Blackburn Rovers in January 2009.
However he failed to establish himself in the first team at Ewood Park and had loan spells with Blackpool, Motherwell, Oldham and Aberdeen before joining Sheffield United last summer.
Crystal Palace had failed with a bid for Blackman, and Blades boss Danny Wilson admits he could not stand in the player's way once a Premier League club made an offer.
"From our position, it is virtually impossible to hold people back when the Premiership comes calling and this is a great opportunity for Nick," said Wilson.
"He wants to play at the best possible level, we knew that when we signed him, and he goes with our best wishes. He is a student of the game and will keep learning his trade at Reading."