Alcaraz agreed a deal with Latics prior to playing in the World Cup after his contract with Belgian side Club Brugge had expired.
His performances in South Africa led to suggestions other clubs might try to hijack the deal but Wigan were always confident of landing the 27-year-old and he has now signed a three-year contract at the DW Stadium.
Roberto Martinez said: "It's 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.
"This is a massive boost for the club and we are thrilled to welcome him on board." Martinez was one of a three-strong Wigan delegation stating the case for signing the player at a Wembley hearing today.
Alcaraz joins a strong Latin American contingent at Wigan including Honduras pair Maynor Figueroa and Hendry Thomas and Colombian Hugo Rodallega.
"I am so happy that everything has gone through now," said the World Cup quarter-finalist.
"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."