Caparros who has had stints in charge at Sevilla, Deportivo Coruna and Athletic Bilbao, has signed a contract until the end of the season, the Balearic Islands club said in a statement on their website.
Laudrup, a former Denmark international who played for Barcelona and Real Madrid, clashed with the club's board over transfer policy and said it was better for the team, who are 10th in the table after six matches, if he left.
"We have a young squad but a promising one," Caparros, whom local media reported had asked for a salary of 1.3 million euros, told a news conference.
"We have been excited to see the quantity of installations and the number of youth teams," the 55-year-old added. "We have been gathering data and there are some very promising lads."
Vice president and majority shareholder Llorenc Serra Ferrer added: "His work is marked by his commitment to the youth school. He doesn't just take charge of the first team but is also interested in developing players."
Caparros's most recent coaching job was with Swiss club Neuchatel, whose Chechen businessman owner Bulat Chagaev fired him after five games.
Caparros was dismissed, the fourth coach to be fired since Chagaev took over in May, even though his side were unbeaten in four matches and had climbed off the bottom of the league.
