The 22-year-old attacking midfielder will spend the current Serie A season with the Partenopei after agreeing a long-term contract.
Club president Aurelio De Laurentiis told sscnapoli.it: "El Kaddouri is an important player for us now and will be in the future.
"It only took one minute to agree terms with (Brescia president) Gino Corioni and another minute to reach an agreement with his agent Mino Raiola.
"I have always worked well with Mino because he's an excellent professional."
Belgium-born El Kaddouri left Anderlecht to join Brescia in 2008, where a series of impressive performances in Serie B alerted Italy's top-flight clubs to his ability.
Quoted in the Corriere dello Sport, Raiola told Radio Kiss Kiss Napoli: "He ready to play at a high level.
"I don't like comparing different players but if I had to I would say he resembles Zidane.
"He knows he has to work hard but the players and coach will help him out.
"I believe he is the most talented player in the league.
"For me, Omar is the icing on the cake for Napoli."