FC Twente left the Serbia international out of a friendly match after reportedly agreeing a fee with Saints and the 25-year-old has now finalised his move to the St Mary's Stadium.
Tadic has been identified as a possible replacement for Adam Lallana, who left for Liverpool this summer along with Rickie Lambert.
He has spent two seasons at the Enschede-based outfit, scoring 28 goals in 66 appearances since moving from Eredivisie rivals Groningen.
Tadic becomes a first signing for new manager Ronald Koeman, who needs to strengthen his squad after Luke Shaw also departed to Manchester United, while fellow defender Dejan Lovren has also been linked with a move to Liverpool.
Feyenoord striker Graziano Pelle and Swedish winger Nabil Bahoui are thought to be on Koeman's shortlist as he searches for more recruits this summer.
Tadic is delighted to have made the move to Southampton, telling the club’s official website: “It is a really nice feeling to sign. This is a really nice club of which I have heard a lot of good things about.
“I have already seen the beautiful training centre and there are lots of nice people that work here including the coaches so I am really happy to be here.
“I watched a lot of [Southampton’s] games last season and saw that the club plays really nice football which will suit me because I like to play in the same way.
“The manager obviously knows me from the Dutch league so, when he called me and told me his plan, it was an easy decision to make.
“I know the manager well because he is one of the biggest Dutch legends in football – everyone knows him.
“He is a really good coach and you can always expect his teams to play well because he is leading them and because he is so good tactically. I am really excited to start playing for the club.”
Koeman also feels the Tadic deal shows that Southampton have lost none of their ambition.
He said: “It was very important to get this signing done – not only for me, but for the rest of the squad and for our fans. It’s fantastic news.
“We’ve lost some good players but we want to continue the ambition and philosophy of the club, so it’s a great signal to have brought in our first player.
“He’s a great player. I know him very well from Holland, where he had a great season last year.
“We now look forward to bringing in more players because we want to continue and maybe even better what Southampton did last season.”