"Gary is a leader and he is exactly the right character we need at the club," the manager told the club's official website, www.wiganlatics.co.uk.
"He is a commanding defender who will lead by example on and off the pitch.
"He has been part of a winning team at Celtic and brings with him great experience, having won league titles and cups and played in the Champions League.
"He is a winner and will become a huge asset for Wigan Athletic."
Caldwell said, "I feel like I'm coming into the best years of my career - as a defender once you get into your 30s I think you do your best stuff.
"Hopefully Wigan have got my best years and I'll do well for the club."
He described leaving Celtic - the club he supported as a boy - as a "wrench" but was lured by the prospect of playing in the Premier League and was persuaded to move to the DW Stadium by the enthusiasm and drive of Martinez.
"The manager made it quite clear what his ambitions are for this club and how much he wanted to bring me here," he added.
"To play in the Premier League has always been an ambition of mine but I know how tough it's going to be to get in the side and I need to focus on winning a place and doing the best I can for my new club.
"It's a massive wrench for me to leave a club like Celtic but I want to thank the club and all the fans for the support they've given me in my time there.
"But I'm a Wigan player now and I can't wait to get started in the Premier League."
Caldwell is under no illusions at the difficulty Wigan face in preserving their top-flight status.
"You look at the league table and it's very tight," he added.
"But there are a lot of teams worried and it's going to be a dogfight right until the very end.
"There's some great players in this team and we've got a squad that's good enough to stay in the Premier League and progress from there."