The striker arrives at St Mary's on a four-year deal for an undisclosed club-record fee, rumoured to be £15million.
Although born in Argentina, Osvaldo has been capped for Italy at both U21 and senior international levels.
And Osvaldo will now be reunited with Mauricio Pochettino, who was his manager during a successful 18-month spell with Spanish side Espanyol.
"Southampton football club is delighted to announce the signing of Italy striker Pablo Daniel Osvaldo," a statement from Saints read.
"Osvaldo today agreed terms on a four-year contract with Saints and moves from Serie A side AS Roma."
The 27-year-old will be officially presented as a Southampton player on Monday, and he is expected to make his debut next Saturday against Sunderland.
Saints have already spent £12.5m on midfielder Victor Wanyama, who was signed from Celtic in July, as well as investing £8.5m in Lyon's Bosnia and Herzegovina international centre-back Dejan Lovren.