Everton bring in two more Wigan old boys
Martinez, who left relegated Wigan at the end of last season, also bought Ivory Coast striker Arouna Kone from the English FA Cup holders on Monday.
Paraguay's free-agent defender Alcaraz, 30, has agreed a two-year deal at Goodison Park, the Premier League club said on their website.
Martinez first signed Alcaraz, who missed much of last season through injury but played in the FA Cup final victory over Manchester City in May, from Belgian side Club Bruges in 2010.
The player appeared in the 2010 World Cup and helped his country to the final of the 2011 Copa America.
The 23-year-old Robles played the second half of last season on loan at Wigan.
"The goalkeeper... will return to play in the Premier League," said Atletico Madrid in a statement.
Joel was part of the Spain squad that won the European Under-21 Championship in Israel last month.
Martinez has taken over at Everton from David Moyes who left for Manchester United when Sir Alex Ferguson retired in May.