"Felipe has great qualities. He is one of the world's top coaches with a record of success at country and club level," Chelsea said in a statement.
Carlo Ancelotti, Mark Hughes and Roberto Mancini had also been linked with the job.
Chelsea added: "He gets the best out of a talented squad of players and his ambitions and expectations match ours. He was the outstanding choice.
"Out of respect for his current role and to ensure minimum disruption to this work there will be no further comment from Chelsea nor from Felipe about his new role until his employment with us commences."
