The 25-year-old Serbia international scored 16 goals in 33 league games last season as Twente finished third behind Ajax and Feyenoord in the Dutch league.
Tadic is the Saints' first signing since Ronald Koeman replaced Mauricio Pochettino as manager in June.
"It was very important to get this signing done - not only for me, but for the squad and our fans," Koeman said.
Koeman wants to bolster his squad following the sales of defender Luke Shaw, midfielder Adam Lallana and striker Rickie Lambert.
Tadic, who Twente signed for £6.1m from FC Groningen in 2012, can play on either side of midfield and is viewed as the ideal replacement for Lallana, who joined Liverpool in a £25m deal at the start of the month.
"This is a really nice club of which I have heard a lot of good things about," said Tadic.
"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."
Koeman feels Tadic's arrival will act as a "great signal" of Southampton's intent to move forward following last season's top-10 finish and the departure of three key players.
"We have lost some good players, but we want to continue the ambition and philosophy of the club," he said.
"We now look forward to bringing in more players because we want to continue and maybe even better what Southampton did last season."
Saints centre-back Dejan Lovren remains a target for Liverpool, who had a £20m bid for the player rejected last week.
Southampton have signed FC Twente attacking midfielder Dusan Tadic for an undisclosed fee, believed to be £10.9m.