The 24-year-old has signed a four-year deal after a ‘substantial’ undisclosed fee was agreed between the two clubs, believed to be around £8m.
It surpasses the amount paid to Queens Park Rangers earlier this summer for Luke Freeman, which was understood to be in excess of £5m.
Robinson has joined up with the Blades in the Algarve for their summer training camp but will not feature in Friday evening’s friendly with Real Betis.
The Republic of Ireland international started his career with Aston Villa, making five substitute appearances for the West Midlands side including four in the Premier League.
He made three loan switches to Preston and one to Bristol City before moving to Deepdale in a permanent deal three years ago.
In total he made 160 appearances for Preston, scoring 41 goals.
Robinson was with Preston in their own pre-season training camp in the Republic of Ireland up to Thursday before travelling to Sheffield for a medical and then on to Portugal to join up with his new team mates.