The 29-year-old will link up with former Chelsea manager Jose Mourinho at Real Madrid.
Mourinho brought Essien to Stamford Bridge in 2005 from Lyon.
Essien was also linked with a move to Arsenal on transfer deadline day.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.