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Smalling, who joined United in 2010, has made over 300 appearances for the club in all competitions but has found himself out of favour at the Old Trafford club this season, especially after the arrival of Harry Maguire.
United boss Ole Gunnar Solskjaer had said at a news conference earlier on Friday that he could not promise Smalling regular game time as he had a number of centre backs to choose from.
"Chris fancied the chance to go over there, it's a new experience, new adventure," Solskjaer told the club's media channel.
"He'll come back better for it because it's a big club, it's a good league. There aren't too many English players who have been playing in Italy so I think he'll enjoy it."
Smalling is United's second senior player to leave the club on loan after forward Alexis Sanchez sealed a loan move to Inter Milan on Thursday.
"This is the perfect opportunity for me. The chance to experience a new league, with a big team that has got big aspirations is exactly what I needed," Smalling said.
"Hopefully I can hit the ground running. I'm looking forward to joining up with my teammates."
While the Premier League transfer window closed on Aug. 8, a day before the season kicked off, the European window is open until Sept. 2.
Customers can earn miles with every purchase made with any linked payment card across all Union Coop stores and online
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