The Blades, third in the table and six points behind leaders Leeds United, had been chasing the 26-year-old since last summer.
Hogan, on loan for the rest of the season from Aston Villa, joins fellow new signings Kieran Dowell and Gary Madine at Bramall Lane as United seek a place in the Premier League.
“We recognised what we needed,” said Wilder, when asked about his sixth window at the helm of United. “We have had to be patient with targets, such as Kieran and Scott.
“But I am delighted with the three players we have brought in. We have had a really good January window and we have got options at the top of the pitch.”
Leeds were still hoping to add to their own attacking options but talks with Swansea City over a possible loan deal collapsed shortly before the 11pm deadline.
The pursuit of James by Leeds came at the end of a busy day in the county as Steve Bruce’s unveiling at Sheffield Wednesday was followed by the capture of Wolverhampton Wanderers full-back Dominic Iorfa.
Newcastle United duo Achraf Lazaar and Rolando Aarons later sealed their own moves to Hillsborough.
Bradford City saw two players head out as manager David Hopkin pulled off the notable coup of landing Jacob Butterfield, the former Huddersfield Town midfielder who joined Derby County for around £5m in 2015, and securing the return of Billy Clarke from Charlton Athletic.
Barnsley were also active in the final few hours of the window, sealing a permanent deal to sign Middlesbrough striker George Miller. The 21-year-old will remain at Valley Parade, where he spent the first half of the season on loan from Boro.
Hull City signed Liam Ridgwell as a free agent, the 34-year-old having left MLS side Portland Timbers in December.
Leaving the county yesterday were Leeds duo Tom Pearce and Sam Dalby to Scunthorpe United and Morecambe respectively.
Ricky Holmes left Bramall Lane for Gillingham, while Boro loaned youngsters Stephen Walker and Hayden Coulson to Milton Keynes Dons and Cambridge United respectively.
The county’s busiest club on deadline day was Bradford. As Jordan Gibson and Ryan McGowan headed out to Stevenage and Dundee respectively, Clarke and Butterfield arrived to bolster a fight for League One survival that will still feature Miller after Barnsley agreed for the striker to remain at Valley Parade despite agreeing a permanent deal to sign him from Middlesbrough.
“I have kept a close eye on Bradford over the last couple of seasons and I know where we are at,” said Clarke, who left Valley Parade in the wake of City’s League One play-off final defeat to Millwall in 2017.
“I have really missed it. My family still live up here and every time I drive past the stadium I miss the feeling I used to get when you run out on the field.”
Bradford-born Butterfield, meanwhile, added: “I want to make an impact straight away. There is a great deal of quality and, in recent weeks, the team has been in good form.”
Doncaster Rovers were another who had a productive end to the window despite manager Grant McCann making no fresh additions to a squad handily placed for a concerted push for the play-offs.
The reason for Rovers’ satisfaction was the successful rebuffing of Sunderland’s late interest in striker John Marquis, the Black Cats understood to have made a seven-figure bid for the top scorer at the Keepmoat Stadium.
Transfer analysis: Page 24