Speed will join Brian Robson's side this week on an 18 month deal - and is expected to turn out for the Blades against Wolves at Molineux on New Year's Day.
The midfielder will also have a 12 month coaching option that he can take up after that.
He will sign on a short term loan deal, before the signing is made permanent for a fee of around £250,000.
Bolton boss Gary Megson was quick to praise the veteran midfielder after the move was announced: "While we don't want to lose someone of his undoubted talent and ability it is a good move for him and I am sure he'll do well at Sheffield."
Meanwhile the Blades are close to capturing Manchester United's Phil Bardsley on a permanent deal, for around £1 million.