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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.