It was revealed last week that Biglia, 27, had agreed to leave the Brussels club and sign for the Coppa Italia winners.
Biglia linked up with his new team-mates at their pre-season training camp on Sunday and his transfer has now been formalised by the Stadio Olimpico outfit.
The Argentinian joins on a five-year contract after enjoying significant success in the Belgian capital, where he won four league titles.
He was previously linked with the likes of Arsenal and Inter before the start of the 2012-13 campaign, but stayed at the Constant Vanden Stock Stadium to help them oust Zulte-Waregem and Club Brugge and seal another domestic crown.
Biglia made 51 appearances for Anderlecht last term, scoring five goals.
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