The 27-year-old signed a three-year contract after being granted a work permit.
Alcaraz was available on a free transfer after his contract with Belgian side Club Brugge expired at the end of last season.
“It is fantastic news that we can finally confirm the arrival of a defender who I feel was one of the very best at this summer’s World Cup,” Wigan boss Roberto Martinez told Wigan’s official website.
“This is a massive boost for the club and we are thrilled to welcome him on board.”
“I am so happy that everything has gone through now,” said Alcaraz.
“I want to thank Roberto and the club for all the hard work to get me to Wigan and now I just want to play football.
“The Premier League is a big challenge for every player and I can’t wait to get started.”
