After Southampton revealed the Italy international had put pen to paper on a four-year deal, his former employers in the Italian capital released the details of a deal initially worth £12.9million.
That figure could rise by another £1.7million dependent on Osvaldo's performances at St Mary's.
The fee for the 27-year-old, who is due to be presented to the media tomorrow, exceeds the £12.5million they forked out last month to bring midfielder Victor Wanyama from Celtic.
"Southampton football club is delighted to announce the signing of Italy striker Pablo Daniel Osvaldo," a statement on the club's official website said.
"Osvaldo today agreed terms on a four-year contract with Saints and moves from Serie A side AS Roma.
"The frontman is expected to be available for next Saturday's Barclays Premier League game against Sunderland at St Mary's, and will be officially presented as a Southampton player tomorrow."
Roma confirmed the details of the deal in a statement on their official website.
"AS Roma announces that it has signed an agreement with Southampton Football Club for the outright sale of the rights to the player Pablo Daniel Osvaldo for an amount of 15.1million euros," the statement read.
"The agreement also provides for the receipt of a variable fee, up to a maximum of 2million euros. These bonuses are linked to the achievement of the player and performance-based goals."
Osvaldo worked with Southampton manager Mauricio Pochettino when the pair were at Espanyol, although getting him to the south coast took some persuasion.
The Argentina-born forward had been linked with Barclays Premier League rivals Manchester City and Tottenham, before eventually agreeing to commit his long-term future to the Saints.
Osvaldo, who has nine Italy caps, becomes Southampton's third signing of the summer, following an £8.5m move for Lyon defender Dejan Lovren and the signing of Kenya midfielder Wanyama.
Southampton won their opening match of the season at West Brom on Saturday, with a late Rickie Lambert penalty securing a 1-0 victory.