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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.