Orsic has joined the Saints for a reported £8m after impressing for Croatia at the 2022 FIFA World Cup in Qatar.
Orsic played six times at the World Cup and scored the winner against Morocco in third place play-off game.
The 30-year-old forward has spent the last four-and-a-half-years with Dinamo Zagreb, scoring 91 goals in 216 games.
Orsic has signed a two-and-a-half-year contract with Nathan Jones' side, who are bottom of the Premier League table with one win in their last 13 games.
Jones said: ‘Mislav is a significant addition to our squad and I’m delighted we have been able to get him in so quickly this month.
‘He’s a serious attacking threat and I’m sure anyone who has followed his progress or saw what he achieved at the World Cup will realise the talent he has. We’re excited to have him here.”
Orsic added: ‘I feel very happy to be here, I think it’s a dream for every football player to come to play in the Premier League and I’m here, I’m ready, I’m motivated and I hope that I will help the team to achieve their goals.
‘When I come here to the camp, it’s amazing, and I’m sure I will really enjoy my time here. Now it’s a little bit of a difficult situation for the club, but I think we need to stay together.
‘We have only one plan – everybody to stay in the Premier League. We need to work hard every day and I hope that at the end of the year we will be happy.’
