Mousset agreed a three-year contract with the newly-promoted Premier League side, who are reported to have paid £10 million to complete the deal.
"For the third time this summer, the Blades have smashed the club's transfer record," United announced on their official website.
"French striker Lys Mousset has signed a three-deal with the Blades after an undisclosed fee with AFC Bournemouth was reached for his services."
Mousset joined Bournemouth from Le Havre in 2016 for £5.7 million, but was mainly restricted to the role of substitute.
The 23-year-old, who scored five goals in 71 appearances for the Cherries, is the Blades' fifth signing since winning automatic promotion to the Premier League last season.
They set a new transfer record by signing Callum Robinson from Preston earlier this month, having already broken it once to bring Luke Freeman to Bramall Lane from QPR.
United have also signed former Manchester United forward Ravel Morrison and Everton defender Phil Jagielka.