The Blades reportedly paid £10 million ($18 million) to secure the Frenchman and have tied him to a three-year deal.
The fee eclipses the club's outlay on Luke Freeman and Callum Robinson, who are said to have joined for £5 million ($9 million) and £8 million ($14.4 million) respectively, earlier in the window.
Mousset, 23, becomes United's fifth new addition since winning promotion to the Premier League.
Manager Chris Wilder said: "Lys is big, quick and a different type of threat at the top of the pitch to what we already have.
"I think he will prove to be a great fit for us and the fact that he selected us above other options shows he's hungry to do well.
"It is a fantastic bit of business for us in the current market and we are looking forward to him joining up with the squad."
Mousset struggled for goals at Bournemouth after joining from Le Havre in 2016.
The former France Under-21 player netted three in the Premier League during his stay at the Cherries, appearing almost exclusively as a substitute under Eddie Howe.