Chelsea had been after an English goalkeeper but gave up after a bid for John Ruddy was rejected and other targets voiced concerns over a lack of first team football on offer.
Schwarzer leaves Fulham to join Chelsea as he bids to play in the World Cup next year for Australia.
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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.