Alcantara has long been expected to join Premier League champions Manchester United, but has now instead joined the Champions League winners.
The youngster will link up with former Barcelona boss Pep Guardiola at Bayern Munich.
Bayern Munich have agreed to pay a fee of 25 million euros for the Spain Under-21 midfielder.
Thiago will have a medical in Munich in the next few days before signing a four-year contract with Bayern, the club confirmed on their website.
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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.