The Serbia international has developed into one of the Eredivisie's best players in recent years, and will move to the 2010 champions at the end of the season
The 23-year-old left winger was previously linked with Roma and Borussia Monchengladbach, but preferred to stay in the Eredivisie and has now signed a three-year deal with Twente, with an option for two more seasons.
The Enschede side were keen to add some more creativity to their attack and head coach Steve McClaren had earmarked Tadic as the perfect addition to his squad.
"He's a fantastic player who can add a lot to this team," said McClaren.
Groningen director Hans Nijland also commented on the move, saying: "Tadic's transfer to Twente is one of the biggest domestic transfers in the history of Dutch football."
Groningen have not wasted any time in finding a replacement for Tadic as they have secured the services of promising youngster Filip Kostic from Radnicki for a fee of €1.25m.
The 19-year-old winger had also attracted the interest of Udinese, Tottenham, Anderlecht, Club Brugge and Porto, but has opted to join the Dutch outfit instead at the end of the 2011-12 campaign.
Kostic, who has represented Serbia at Under-19 level, has signed a contract until the summer of 2015, with an option for two additional seasons.