The 30-year-old Paraguay international has signed a two-year deal at Goodison Park and is the second former Latics player captured by Roberto Martinez in as many days following the arrival of striker Arouna Kone on Monday.
Alcaraz suffered a difficult campaign last season as a groin injury sustained on international duty in August ruled him out for six months and Martinez has said he believes Wigan would not have been relegated had he stayed fit.
Six of his 14 appearances last season resulted in clean sheets, including a fine display when Wigan knocked Everton out of the FA Cup on their way to the trophy.
Alcaraz has indicated he had offers from abroad before joining Everton but he wanted to stay in England's top flight.
He told Everton's official website: "We talked to a lot of clubs but I was always interested in staying in the Premier League. I like this competition and at this moment in my career I thank Everton for giving me this opportunity to continue in the Premier League."
Alcaraz is now looking forward to a reunion with Martinez, as he said: "I know him really well and he knows me very well also.
"We had a very good relationship in the three years at Wigan and I want to continue that. Nothing is going to change, he is very professional."