Morgan has taken the reins on a temporary basis at Bramall Lane for the second time in recent years after David Weir was sacked last week.
The 35-year-old, who oversaw the Blades' 3-2 defeat to Coventry on Sunday which left the south Yorkshire club rooted to the bottom of the Sky Bet League One table, did not expect to still be in charge ahead of this weekend's visit of Port Vale and has enlisted the help of the experienced Wadsworth.
"After the game on Sunday I expected there to be a new manager in place early in the week but that never materialised so I asked the board if we could do it (bring in Wadsworth)," said Morgan.
"I felt I needed some experience and another voice and thankfully the board gave the go-ahead.
"I've known Mick a long time and he has a great pedigree. He is a great coach but he has also managed and he has vast knowledge and experience ranging from non-league right up to World Cup campaigns.
"He's also a local man and he knows what is expected and wanted at this club and I'm delighted he's agreed to come in and help me, and he was very happy and keen to do so."
Barnsley-born Wadsworth has held positions at the likes of Carlisle, Scarborough, Huddersfield and most recently Hartlepool as well as taking charge of the DR Congo national team and Portuguese club Beira-Mar.
He worked with England under the late Sir Bobby Robson and later Graham Taylor between 1988 and 1992.
- Sports & Recreation