The Premier League side have tracked the young German forward for some time.
The fee is reported to be just under £20 million, and Schurrle becomes Jose Mourinho’s first signing in his latest spell at Stamford Bridge.
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Who of Europe’s top strikers will move to England this summer?
After a dreadful start to their Bundesliga campaign, Borussia Dortmund appear to have weathered the storm after going five matches without defeat.