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Coach Christophe Galtier's star-studded team that includes striker Kylian Mbappe and world champion Lionel Messi failed to score against Bayern over two legs, losing 3-0 on aggregate.
Brahim Diaz's goal gave AC Milan a 1-0 win over Tottenham Hotspur in their last-16 first leg at the San Siro.
The Bayern Munich forward had picked up a leg injury last week.
The 22-year-old Bayern Munich left-back will be one of the stars to watch out for in Qatar.
Bayern top Group C on 15 points, five ahead of Inter Milan who also reached the knockout stage after a 4-0 win against Viktoria Plzen, a result that eliminated Barcelona in the group stage for the second year in a row.
For Bayern the win could not have come at a better time, following three consecutive draws in the Bundesliga.
Real will take on RB Leipzig, Shakhtar Donetsk and Celtic in the group stage.
Lewandowski, who scored 344 goals for Bayern in 375 appearances, joined Barcelona in a deal worth 45 million euros earlier this month, after forcing a move from the German club.
Lewandowski, who had 12 months remaining on his Bayern contract, moved to Barcelona in a deal worth 45 million euros and has joined the team on their US pre-season tour.
Spanish media reports that the transfer would cost Barcelona some 50 million euros ($50.4 million).