The 22-year-old joined the Magpies as a trainee in 2009, but made only nine first-team appearances for the club.
Bradford-born Tavernier made his Newcastle debut in a League Cup match against Peterborough in September 2009 but has spent much of his time with the club out on loan.
He has experienced temporary spells with Carlisle, Sheffield Wednesday, MK Dons, Shrewsbury and Rotherham, with whom he won promotion from Sky Bet League One last season.
"It has been a long summer and I've been waiting a long time to finalise the deal," Tavernier told Wigan's official website.
"Now that it has been completed, I'm delighted.
"Wigan Athletic are a Premier League club and I've always known them to be a Premier League club and hopefully I can help get us back where we belong."
Latics manager Uwe Rosler was equally delighted by confirmation of the deal.
“He proved last season what great potential he has by being part of a very successful Rotherham side throughout the season and also in the play-offs.
“He will bring great competition on that side of the field, he is still learning and, at just 22, I feel that we can provide the right sort of environment for him to grow and develop into a really important player for this club.”