The 20-year-old striker has moved to Bramall Lane in a £23.5million deal after The Blades beat off interest from several other Premier League clubs.
“After years of learning and growing at Liverpool the time has come for me to head onto a new chapter," he wrote on social media.
"An emotional thank you to everyone at LFC for their belief and support in me every step of the way, through all the good times and tougher ones as well.
“Huge love to all my teammates, taking me under their wing and pushing me to be better every single day.
“I leave here with special memories and countless learnings. But most importantly, better than I arrived. YNWA."