World football's governing body announced in May they had asked United and Juventus for clarification on all aspects of Pogba's £89.3 million move.
Serie A club announced the arrival of the former Perugia manager on their official website.
AC Milan, Inter Milan and Juventus all want to sign Paris Saint-Germain midfielder Blaise Matuidi this summer, according to agent Mino Raiola.
Torino president Urbano Cairo says there has been no contact with AC Milan over Andrea Belotti, while he has ruled out a return of Joe Hart.
Last week, Raiola told the club that the 18-year-old goalkeeper, who has a year left on his contract, would not be signing a new deal.
Fiorentina have announced the signing of defender Bruno Gaspar from Vitoria de Guimaraes on a five-year contract.