Osvaldo has signed a four-year deal at St Mary's, adding to a fine week for the Saints who kicked off their new Barclays Premier League campaign with a 1-0 win at West Brom on Saturday.
The Argentinian 27-year-old played under Pochettino for just over a season at Espanyol and believes it was a period which produced the best spell of his career so far.
Osvaldo said: "I've worked with Mauricio before and I know him quite well. The season I shared with him at Espanyol was my best season as a footballer in a personal and collective sense.
"It's fantastic to work with Mauricio. He's a great motivator and for me it's very important to work with people who appreciate and respect how I work.
"For some years I've been working with people who don't appreciate how I work as a player, so it's great for me to to be working with people who do appreciate it."
Osvaldo, who has won nine caps for Italy, scored 16 goals in Serie A last year but admitted to a long-held desire to play in the Barclays Premier League, with Tottenham among a number of clubs linked in the summer.
He added: "I've been dreaming about playing in the Premier League and I want to do something important in this league, so I've made this dream come true.
"I've always been a massive fan of the Premier League. The technical level of the league is amazing and it is very dynamic. Overall I'm thrilled to be here."
Osvaldo's arrival takes Southampton's summer spending spree over the £30million mark following earlier deals for Victor Wanyama and Dejan Lovren.