Cannon joins the Blades for a mooted £10m fee. He spent the first half of this season on loan at Championship rivals Stoke City.
Cannon, 22, has signed a four-year contract at Bramall Lane, with an option for an additional 12 months.
"This is a big statement by the owners and shows the ambition of the football club," Blades boss Chris Wilder told the club's website. "Bringing in someone of the calibre of Tom at this time will excite the supporters and energise the group.
"He is of a good age to develop but also has the experience of this level, both important factors. I spoke to Tom in the summer, he's aware that I am a big fan of his talents, I'm delighted he is a Blade and part of our longer-term vision."
Cannon also said: "I am absolutely delighted. I am just looking forward to stepping out at Bramall Lane and getting going," Cannon added.
"Everybody knows the size of the club, and the fanbase. I am just delighted to be here and after speaking to the manager, I heard nothing but good words about the place.
"He (Wilder) just filled me with a lot of confidence which is always nice from a manager. He's just said nothing but good things about the club and the direction he wants to take it moving forward. It was something I really wanted to be a part of."