The 25-year-old joins the Saints for an undisclosed fee, reported to be in excess of £8million, and becomes the first player brought in by new manager Ronald Koeman.
Southampton are looking to rebuild the squad following the sales of key men like Luke Shaw, Adam Lallana and Rickie Lambert after Mauricio Pochettino left to take over at Tottenham.
Tadic said: "It is a really nice feeling, 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."
Attacking midfielder Tadic, 25, scored some 16 times in 33 league games last season for Twente, as the Dutch side finished third behind Ajax and Feyenoord.
Tadic, who has agreed a four-year deal at St Mary's, is confident he has joined a club going places under Koeman, who impressed while in charge of Feyenoord in the Eredivisie.
"I watched a lot of the 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," he added.
"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, meanwhile, feels Tadic's arrival will act as a "great signal" of Southampton's intent to move forwards following last season's top-10 finish and the departure of so many key players.
"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," he said in a statement on the club's official website, www.saintsfc.co.uk.
"We have lost some good players, but we want to continue the ambition and philosophy of the club, so it is 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."
Southampton have also been linked with Lorient defender Bruno Ecuele Manga, who could be seen as cover for wantaway Dejan Lovren.
Liverpool are keen on the Croatia international, and Lovren admits his head has been turned by the Reds interest, with a bid in the region of £18million said to be rejected having fallen way short of the club's valuation.
Source : PA
Source: PA