The move had been held up over the compensation package for Swans assistant manager Graeme Jones and chief scout Kevin Reeves, who have also joined Martinez at Wigan.
"I am delighted to be back at Wigan Athletic, as you know I had a great time here as a player and the club has always been close to my heart," Martinez told the official Wigan website.
"I am looking forward to getting stuck in and taking on teams in the best league in the world.
"I cannot wait for my first game at the DW Stadium, it seems like a long time away but there is a lot of work to do before then.
"The club has done incredibly well over the past five years, firstly getting into the Premier League and staying there, last year not only staying there but pushing higher up the table.
"I want to carry on the good work Steve Bruce did here."