No fee was mentioned for Tadic, who scored 16 league goals for Twente last season, but he is Koeman's first capture since England internationals Rickie Lambert and Adam Lallana left for Liverpool and fullback Luke Shaw joined Manchester United.
The 25-year-old Serbian is a left-sided midfielder noted for his dribbling skills and is seen as a replacement for Lallana, who joined the Merseysiders for a fee British media reported to be 25 million pounds.
Koeman arrived at Southampton in June, replacing Mauricio Pochettino, who moved to Tottenham Hotspur.
"It is a really nice feeling to sign. This is a really nice club of which I have heard a lot of good things," Tadic told the club website.
Koeman added: "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 have lost some good players but we want to continue the ambition and philosophy of the club. He’s a great player. I know him very well from Holland, where he had a great season last year."
(Reporting By Tony Goodson; editing by Toby Davis)
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