Luxemburgo replaces Abel Braga, whose team lost five games in a row to see him lose his job.
Former Brazil and Real Madrid coach Luxemburgo has won five Brazilian titles, with Corinthians, Cruzeiro, Santos and Palmeiras (twice).
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.