The duo, who join fellow new recruit Ryan Leonard at Bramall Lane, were unveiled by Chris Wilder's side this afternoon.
Evans, who has represented Wales at international level, arrives for an undisclosed sum while Wilson will spend the rest of the season in South Yorkshire on loan.
Evans, like Leonard, has agreed a three-and-a-half year contract.
"Lee is a great age with his best years ahead of him. We've watched him and monitored his progress for a while and we're delighted to get him permanently," Blades boss Chris Wilder said.
"He is a young international, he fits in with what we're about and is an excellent player who we hope will add further depth and competition to our midfield."
On Wilson, Wilder added: "James has a fantastic pedigree, having come through the ranks at Manchester United and, importantly, has some good Championship experience.
"He says he is raring to go and is the fittest he has ever been, so couple that with his undoubted ability and desire to impress, then I'm sure he will improve the group."
Wilson has spent time on loan at Brighton and Derby after being scouted by United's Manchester namesakes at the age of seven.