Fyvie, 19, had been on the radar of several English clubs and Dons manager Craig Brown admitted last week he was braced for bids to come in for the midfielder.
And Wigan have won the battle for his signature, with boss Roberto Martinez calling him a "tremendous" prospect.
"I'm excited because we're signing such a strong character and a great personality at just 19 years of age," the Spanish coach said. "He's got a tremendous future in his hands and we're all delighted that he's making a big step forward in his career here at Wigan Athletic.
"He's a bright young man. Technically he's very gifted, enjoys playing in the midfield where he can cover large areas, he's very powerful off the ball and in possession is someone who can read the tempo of the game very well.
"Also you have to remember that for such a young player he's played a lot of games in the SPL at a high standard which shows his maturity."
The 19-year-old midfielder became the youngest ever player to start for the Dons when he made his debut against Hamilton in 2008.
The Scotland Under-19 international made his debut for the Dons at the age of 16 and has already played over 50 league games for the club.