The 34-year-old former Celtic and Middlesbrough midfielder has signed until the end of the season after his contract with MLS side Vancouver Whitecaps was cancelled by mutual consent earlier this month.
Former Blades striker Jonathan Forte returned to Bramall Lane earlier in the day when he signed on loan from Southampton until May.
"We've lost Nick Blackman to the Premier League, but fortunately we've managed to bring in Barry at short notice on a deal until the end of the campaign," Blades manager Danny Wilson told the club's official website.
"When someone of his experience and quality comes along you have to sit up and take notice and I'm delighted a deal can be completed, especially given the fact that he's been back in the country less than a week.
"He gives us options in offensive positions, he will score goals and be a supply line for others."
Robson, capped 17 times by Scotland, began his career at Inverness and moved on to Dundee United in 2003 before securing major deals with Celtic and then Middlesbrough.