Tadic has signed a four-year deal at the club and becomes manager Ronald Koeman's first signing at St Mary's.
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The 25-year-old, who primarily plays as a left winger, enjoyed a stunning season for Twente in 2013-14, scoring 16 goals and providing 14 assists in 33 Eredivisie appearances.
Upon completing his move, he told Southampton'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."
And Koeman also hailed the signing, and hinted at further moves in the close-season.
“It was very important to get this signing done – not only for me, but for the rest of the squad and for our fans," he added. "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.”