The 30-year-old, who has been given a two-year deal, told Wigan's website: "It's great to get to play in the Premier League. It's a big step up.
"Hopefully I can take it in my stride and do well. Just thinking about lining up against some of the best players in the world makes me smile."
Burnley had an estimated £1.25m bid rejected for Scotland but Wigan were always favourites to sign the Trinidad and Tobago international once Roberto Martinez expressed an interest.
"Me and the gaffer were together at Swansea City for two seasons and it's exciting to be able to team up again here," added Scotland.
"He likes his team to get the ball down, move it around and keep possession. He wants his players to be in complete control of the game and because of this tactical approach to the game Swansea were able to do so well last season.
"I'm sure he's going to try and introduce that kind of attractive style of play here and I can't wait to be a part of it."