The 24-year-old has signed a four-year deal at Bramall Lane after leaving Preston North End in a deal believed to be worth in the region of £6-8m.
Robinson becomes the third signing of the summer by Chris Wilder, his fee exceeding the £5m paid to prise Luke Freeman away from Queens Park Rangers earlier this month.
"Callum fits into our structure perfectly as we look to Championship players who we feel can be successful at Premier League level," said manager Wilder. "Callum is someone who was on our radar a number of years ago and he has progressed how we thought he would and hopefully there is plenty more to come.
"I feel Callum is a great age and what we have paid represents great value in the current market."
Robinson netted 13 times for North End last season despite missing a portion of the campaign through injury. He had just entered the final year of his contract at Deepdale.
He will not feature in tonight's friendly against Real Betis at Estadio Algarve but it is understood he is in Portugal after completing his switch.