Midfielder Evans has joined on a three-and-a-half year deal from Championship rivals Wolves, while striker Wilson has signed on for the remainder of the campaign on a temporary deal.
Blades boss Chris Wilder has welcomed his latest arrivals and he feels both can play key roles in the remainder of the campaign.
On Wales international Evans, Wilder told the club's official website: "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.
"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, he added: "James has a fantastic pedigree, having come through the ranks at Manchester United and, importantly, has some good Championship experience [during loan spells with Brighton and Derby].
"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."