Martinez, who succeeded David Moyes at Goodison Park, rekindled his working relationship with the 30-year-old defender having signed him while at Wigan.
The Paraguayan centre-back joined the club on a two-year deal as a free transfer after his contract at the DW Stadium expired and Martinez is confident Everton have secured a major coup.
|22/1||Everton are 22/1 with Coral to finish in the top four
"He comes in a perfect moment after three seasons in the Premier League. At his age, he is a commanding figure, a real leader within himself with really high standards.
"He's someone who is going to fit in extremely well with what we have in our dressing room.
"He's an exciting prospect and we've been fortunate enough to get him at the end of his contract so as a free transfer, he's going to be a very important addition at the back."
Alcaraz spent three years at Wigan after joining from Club Brugge in 2010, but only started eight Premier League games in an injury-hit 2012-13 campaign.
His addition marks Martinez's third signing in two days, with all three having come from his former club as he secured the services of Arouna Kone and Joel Robles.