The 21-year-old is set for a £2million return to Brammall Lane, just two years after the Iron bought him from the Blades for £100,000.
He had two freescoring seasons at Glanford Park, setting a new club record of 32 goals in a season as the Iron won the League One title at a canter last term.
"Billy did not want to leave, he just wanted the chance to play first-team football and I must say Scunthorpe have done a great job," Robinson told PA Sport.
"The agreement gave him the opportunity to develop far faster than he would have here.
"It shows that the system and development of young players in this country falls down at the middle stage, where developing players do not or cannot get enough competitive football.
"To do that they have to go out on loan or transfer to a club where they do get regular games."
BBC Radio Humberside report midfielder Ian Ross and winger Jonathan Forte are poised to come to Glanford Park as part of the deal.