The 22-year-old striker has signed a two-year contract with the Blades for an undisclosed fee.
Blackman arrived at Rovers in January 2009 after successful trial, quickly establishing himself with the Reserves.
In search of first team football he enjoyed loan spells with Blackpool, Oldham Athletic and then in the SPL with Motherwell and Aberdeen.
Having returned to Rovers, Nick made his first senior appearance in the opening league game last season against Wolverhampton Wanderers. He would go onto make a further two starts in the League Cup.